Distance Time Graph and Velocity Time Graph - Definition, Examples, FAQs

Edited By Vishal kumar | Updated on Jul 02, 2025 05:06 PM IST

More importantly, for physicists, distance-time and velocity-time graphs are useful illustrations in describing as well as representing visual motion behaviours, through a change of position or speed with time, so that they understand the pattern of movement and have some idea about the future position.

Distance Time Graph and Velocity Time Graph

In this article, we will discuss the distance-time graph for uniform motion and the velocity-time graph for uniform motion, covering the uses of these motion graphs, how they represent uniform and non-uniform motion, and the concept of the graphical representation of motion for Class 9 students.

What is a Distance Time Graph?

A distance-time graph represents the distance covered by an object from the starting point against time. In the graph, time is taken alongside the X-axis and distance is taken alongside the Y-axis.

Uses of Distance-Time Graph

The graph of distance and time is used to determine the position of an object at any time in the given time interval.
To determine the speed of an object at any time in the given time interval.

The graph of uniform and non-uniform motion of an object can be studied on the basis of a distance-time graph. Let us now draw a distance-time graph for uniform and non-uniform motion to understand it clearly.

Point to be noted: The area under the distance-time graph is a nonentity

Equation of distance time graph= Slope = speed = distance/time

Also read -

For uniform motion:

Let us study the position-time graph for uniform motion along a straight line. We know, when an object covers the same distances in the same intervals of time, it is said to be in uniform motion.

Let’s take an example of a distance-time graph for uniform motion, a school bus is moving in a straight line and covers the following distances in a given time interval.

information regarding the distance covered by schoool bus in given time.

Fig. (i)

In Fig. (i) First column shows time in unit "seconds" and the second column shows distance in unit "meters ". Now let us draw the distance-time graph for uniform motion, taking time along the X-axis and distance along the Y-axis.

The X-axis scale of the graph is:

1 centimeter = 10 seconds

The Y-axis scale of the graph is:

1 centimetres = 15 meters

d-t graph for uniform motion

Fig. (ii)

What does the distance-time graph represent?

As the distance-time graph of uniform motion is a straight line, distance and time are directly proportional to each other, which means an object covers an equal distance in equal intervals of time in the case of uniform motion. The slope of the straight line in the distance-time graph of an object moving with uniform speed gives the speed of the moving object.

For non–uniform motion:

Let us study the distance-time graph for non-uniform motion along a straight line. We know that when an object covers uneven distances in equivalent intervals of time, it is said to be in uniform motion.

Let’s take an example from the distance-time graph, a car is travelling in a straight line in a non–uniform motion with the following distances in a given time interval.

information regarding a car travelling certain distance in given time.

Fig. (iii)

In Fig. (iii), the first column shows time in unit "seconds" and the second column shows the distance in units "meters ". Now, let us draw a position-time graph, taking time along the X-axis and distance along the Y-axis.

d-t graph for non-uniform motion.

Fig. (iv)

The X-axis scale of the graph is:

1centimeter = 5 seconds

The Y-axis scale of the graph is:

1 centimetres = 5 meters

What does the distance-time graph represent?

As the distance and time graph is not a straight line, we can say that distance is not proportional to time. In other words, in the case of a distance-time graph for non-uniform speed, distance does not change uniformly with time.

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Distance-time graph for a body at rest:

In the distance-time graph for the body at rest, the graph will show a line parallel to the x-axis. The parallel line shows that the time is changing, but the position of the body is the same.

Let us now draw a distance-time graph for an object at rest.

The parallel line shows that the time is changing but the position of the body is same.

Fig. (v)

Velocity – Time Graph

The velocity-time graph is a graph in which the Velocity varies with time for an object moving in a straight line. In this graph, time is taken alongside the X-axis, and Velocity is taken alongside the Y-axis. This graphical representation of motion is another crucial concept in Class 9 physics, allowing students to understand velocity changes during motion.

Uses of v vs t Graph

To determine the magnitude of the displacement (distance).
To get the information about the acceleration of an object.

Answer to the question of how to calculate distance from a velocity-time graph/ how to find distance from a velocity-time graph: The area enclosed by the velocity-time graph gives the magnitude of displacement. The uniform and non-uniform motion of an object can be studied on the basis of the velocity-time graph for class 9.

Velocity-time relation =

Slope = acceleration = velocity/time

For uniform velocity:

Let us study the velocity-time graph examples to understand uniform motion along a straight line. We know that when an object covers the same distances in the same intervals of time, it is said to be in uniform motion.

Let’s say we have information about a moving car having velocity in unit “meters per second” and time in unit “seconds”. In this graph, time is taken alongside the X-axis, and Velocity is taken alongside the Y-axis.

information about a moving car having

Fig. (v)

Now, let us draw a velocity-time graph for uniform motion in order to understand it further.

The following is the velocity-time graph for uniform velocity.

The X-axis scale of the graph is:

1centimeter = 10 seconds

The Y-axis scale of the graph is:

1 centimetre = 10 meters per second.

v-t graph for the body moving with uniform velocity.

Fig. (vi)

If the object moves in uniform motion, then the Velocity vs time graph will show a line parallel to the x-axis (i.e. time interval).

What can we understand from this graph?

This is a constant velocity graph. We know that acceleration is defined as the rate of change of velocity, but here we do not have any change in the velocity throughout, so we can say there is no acceleration. So it is a zero acceleration graph.

So whenever we notice a velocity-time graph parallel to the x-axis, we can conclude two things: first, the body is moving with uniform velocity, and second, the acceleration is zero.

For uniform accelerated motion (increasing):

Let us study the velocity-time graph for uniform acceleration motion.

information about a moving car

Fig. (vii)

Now, let us plot the vt graph for uniform motion in order to understand it further.

The following is a velocity-time graph of uniform motion.

v-t graph in which the velocity is increasing uniformly with time

Fig. (viii)

The X-axis scale of the graph is:

1 centimeter = 10 seconds

The Y-axis scale of the graph is:

1 centimetre = 5 meters per second.

What does the velocity-time graph represent?

We get an increasing graph, or we can say again we get a straight line, but this time it is not parallel to the x-axis. It is inclined to the x-axis. In the velocity-time graph of uniform acceleration, we can see that the velocity is increasing uniformly with time, and we get a positive acceleration graph.

The graph for uniform acceleration, or uniform acceleration graph, or uniform motion graphs, or uniformly accelerated motion graph, concludes that the body is moving with uniformly increasing velocity and the acceleration of a particle is increasing linearly. A particle starts from rest. Its acceleration versus time graph gives the maximum velocity of the particle.

A force-time graph for the motion of a body gives the change in linear momentum of the body.

For uniform accelerated motion (decreasing):

Let us study the velocity-time graph for uniformly accelerated motion.

Let’s say we have information about a moving car having velocity in unit “meters per second” and time in unit of “seconds”. Let’s draw the velocity-time graph for a car moving with uniform acceleration. In this graph, time is taken alongside the X-axis, and Velocity is taken alongside the Y-axis.

a body which is having uniformly decreasing velocity

Fig. (ix)

What does the velocity-time graph represent?

Now, let us try to infer what this graph is telling us. This velocity-time graph is again a straight line, but it has a negative slope. This type of velocity-time graph means that there is a body that is having uniformly decreasing velocity. Hence we have the negative (constant) acceleration, or the acceleration is retarding.

For non-uniform accelerated motion:

Let us study the velocity-time graph for non-uniform motion.

Say we have information about a moving car having velocity in unit “meters per second” and time in unit “seconds”. Let’s draw a velocity-time graph for non-uniform acceleration. In this graph, time is taken alongside X-axis and Velocity is taken alongside the Y-axis.

the body is moving with non - uniform velocity

Fig. (x)

By studying these graphs of motion for Class 9, students can grasp fundamental physics concepts related to motion and acceleration. The graphical representation of motion simplifies complex ideas, making them accessible and visually comprehensible.

Comparative study of Distance-time and Velocity-Time Graphs

The table shown below represents a comparative study of both distance-time and velocity-time graphs:

Representation	Distance-time graph	Velocity-time graph
X-axis	Time	Time
Y-axis	Distance	Velocity
Horizontal line	Indicates that the object is stationary	indicates constant velocity
Curved line	Indicates that the object is changing speed	represents changing acceleration
Slope	represents the speed of the object	represents acceleration
Steeper slope	represents the faster speed	indicates a greater acceleration
Area under the curve	-	represents displacement

Frequently Asked Questions (FAQs)

1. What is the physical significance of velocity time and distance time graph according to graphical representation of motion class 9?

Physical significance of distance time graph- The graph of distance and time is used to determine the position of an object at any time in the given time interval.

Physical significance of velocity time graph - To determine the magnitude of the displacement (distance).

2. What will be the gradient of the velocity time and distance time graph?

The gradient of distance-time is equal to the velocity of an object.

The gradient of a velocity-time graph gives the acceleration of an object.

3. What is a negative gradient?

Negative gradient means that the slope of the graph is downwards.

4. What does the area under velocity time graph give?

The area enclosed by the velocity-time graph gives the magnitude of displacement.

5. What do you mean by uniform decreasing accelerated motion?

Uniform decreasing accelerated motion means that there is a body which is having uniformly decreasing velocity.

6. What does the area under the curve of distance-time graph represents?

The area under the curve of the time-distance graph represents no specific quantity.

7. What is a VT graph?

A velocity-time (VT) graph is a graph that compares how velocity is varying with respect to time. This graph also provides the information of displacement and acceleration of the object.

8. What does a DT graph shows?

A distance-time (DT) graph is a graph that basically compares how distance is varying with respect to time. This graph also provides the information of speed.

9. Can acceleration be negative?

An object having negative acceleration, also known as deceleration, means that the object is moving in a positive direction and reducing velocity (slowing down) or moving in a negative direction and increasing velocity (speeding up).

10. What is zero acceleration?

Zero acceleration means velocity is not changing with time.

11. What is a velocity-time graph?

A velocity-time graph is a visual representation of an object's motion, showing how its velocity changes over time. The horizontal axis represents time, while the vertical axis represents velocity. This graph helps us understand an object's speed and direction at different points during its journey, as well as its acceleration.

12. How can you determine acceleration from a velocity-time graph?

Acceleration can be determined from a velocity-time graph by looking at the slope of the line. A constant positive slope indicates positive acceleration, a constant negative slope indicates negative acceleration (deceleration), and a horizontal line (zero slope) indicates zero acceleration (constant velocity).

13. What does the area under a velocity-time graph represent?

The area under a velocity-time graph represents the displacement of the object. This is because displacement is the product of velocity and time, which corresponds to the area of the region bounded by the velocity curve and the time axis.

14. Can velocity be negative on a velocity-time graph?

Yes, velocity can be negative on a velocity-time graph. A negative velocity indicates that the object is moving in the opposite direction to the one defined as positive. On the graph, negative velocity values appear below the time axis.

15. What does the slope of a distance-time graph represent?

The slope of a distance-time graph represents the velocity of the object. A steeper slope indicates a higher velocity, while a gentler slope indicates a lower velocity. The sign of the slope (positive or negative) indicates the direction of motion relative to the chosen reference point.

16. What is a distance-time graph?

A distance-time graph is a visual representation of an object's motion, showing how its distance from a starting point changes over time. The horizontal axis represents time, while the vertical axis represents distance. This graph helps us understand an object's position and speed at different points during its journey.

17. How can you determine if an object is moving or stationary from a distance-time graph?

On a distance-time graph, a horizontal line parallel to the time axis indicates that the object is stationary, as its distance from the starting point remains constant over time. Any line with a slope (positive or negative) indicates that the object is moving, as its distance is changing with time.

18. Can a distance-time graph have a negative slope?

No, a distance-time graph cannot have a negative slope. Distance is always measured as a positive quantity from the reference point, regardless of the direction of motion. A decreasing distance would be represented by a line with a positive slope moving downward on the graph.

19. What does a curved line on a distance-time graph indicate?

A curved line on a distance-time graph indicates that the object's velocity is changing over time, meaning the object is accelerating or decelerating. The steepness of the curve at any point represents the instantaneous velocity at that time.

20. How are distance-time and velocity-time graphs related?

Distance-time and velocity-time graphs are closely related. The slope at any point on a distance-time graph gives the instantaneous velocity, which corresponds to the y-value at that same time on a velocity-time graph. Conversely, the area under a velocity-time graph gives the displacement, which is the change in distance on a distance-time graph.

21. What does the area under an acceleration-time graph represent?

The area under an acceleration-time graph represents the change in velocity over the given time interval. This is because velocity is the integral of acceleration with respect to time, which is graphically represented by the area under the acceleration-time curve.

22. How can you tell if an object is accelerating from a velocity-time graph?

On a velocity-time graph, acceleration is indicated by a change in velocity over time. This appears as a line with a non-zero slope. A positive slope indicates positive acceleration (speeding up), while a negative slope indicates negative acceleration (slowing down).

23. What does a horizontal line on a velocity-time graph represent?

A horizontal line on a velocity-time graph represents constant velocity or zero acceleration. This means the object is moving at a steady speed in the same direction, neither speeding up nor slowing down.

24. Can a velocity-time graph have vertical lines?

No, a velocity-time graph cannot have vertical lines. A vertical line would indicate an instantaneous change in velocity, which is physically impossible as it would require infinite acceleration. In reality, velocity changes occur over a finite time interval.

25. How do you calculate average velocity from a distance-time graph?

To calculate average velocity from a distance-time graph, you need to find the total displacement (change in distance) and divide it by the total time elapsed. Graphically, this is represented by drawing a straight line from the start point to the end point of the journey and calculating its slope.

26. What does the y-intercept on a distance-time graph represent?

The y-intercept on a distance-time graph represents the initial distance of the object from the reference point at time zero. If the y-intercept is positive, it means the object started at some distance away from the reference point. If it's zero, the object started at the reference point.

27. How can you identify periods of rest on a velocity-time graph?

Periods of rest on a velocity-time graph are represented by segments of the line that coincide with the time axis (x-axis). During these periods, the velocity is zero, indicating that the object is not moving.

28. What does a straight line passing through the origin on a distance-time graph indicate?

A straight line passing through the origin on a distance-time graph indicates that the object is moving with constant velocity, starting from the reference point (zero distance) at time zero. The slope of this line gives the constant velocity of the object.

29. How can you determine if an object is moving faster or slower at different points on a distance-time graph?

To determine if an object is moving faster or slower at different points on a distance-time graph, compare the steepness of the curve at those points. A steeper section indicates higher velocity, while a less steep section indicates lower velocity. For a straight line, the velocity is constant throughout.

30. How can you tell if an object is moving in the positive or negative direction from a velocity-time graph?

On a velocity-time graph, positive velocity values (above the time axis) indicate motion in the positive direction, while negative velocity values (below the time axis) indicate motion in the negative direction. The direction considered positive is arbitrary but must be consistent throughout the problem.

31. What does a parabolic curve on a distance-time graph indicate?

A parabolic curve on a distance-time graph indicates that the object is moving with constant acceleration. The changing slope of the parabola reflects the continuously changing velocity, which is characteristic of uniformly accelerated motion.

32. How can you determine the direction of acceleration from a velocity-time graph?

The direction of acceleration can be determined from the slope of the velocity-time graph. A positive slope (line tilting upward) indicates positive acceleration in the direction of motion. A negative slope (line tilting downward) indicates negative acceleration or deceleration.

33. What does the intersection of two lines on a distance-time graph represent?

The intersection of two lines on a distance-time graph represents the point at which two objects have the same position at the same time. This could indicate a meeting point if the objects are moving towards each other, or one object overtaking another if they're moving in the same direction.

34. How do you interpret a velocity-time graph where the line crosses the time axis?

When a line on a velocity-time graph crosses the time axis, it indicates that the object's velocity has changed from positive to negative (or vice versa). This means the object has changed its direction of motion at that point in time.

35. What information can you derive from the steepness of a velocity-time graph?

The steepness of a velocity-time graph indicates the magnitude of acceleration. A steeper line represents a greater rate of change of velocity, which means higher acceleration. A less steep line indicates lower acceleration, while a horizontal line represents zero acceleration (constant velocity).

36. How can you use a distance-time graph to determine when an object reaches its maximum distance from the starting point?

On a distance-time graph, the point where the object reaches its maximum distance from the starting point is represented by the highest point on the curve. At this point, the tangent to the curve will be horizontal, indicating momentary zero velocity before the object changes direction or stops.

37. What does a sinusoidal curve on a velocity-time graph represent?

A sinusoidal curve on a velocity-time graph represents periodic motion, such as simple harmonic motion. It indicates that the object's velocity is continuously changing in a regular, repeating pattern, alternating between positive and negative values.

38. How can you determine the total distance traveled from a velocity-time graph?

To determine the total distance traveled from a velocity-time graph, you need to calculate the area under the absolute value of the velocity curve. This includes both positive and negative areas, as distance is always positive regardless of direction.

39. What does a step function on a velocity-time graph indicate?

A step function on a velocity-time graph indicates instantaneous changes in velocity, which are not physically possible in real-world scenarios. This type of graph is often used as an idealized model for situations where velocity changes occur very rapidly, such as in collisions or sudden starts and stops.

40. How can you use a distance-time graph to determine average speed over different intervals?

To determine average speed over different intervals using a distance-time graph, calculate the slope of the line segment connecting the start and end points of each interval. The steeper the slope, the higher the average speed for that interval.

41. What does a velocity-time graph look like for an object in free fall near Earth's surface?

For an object in free fall near Earth's surface (ignoring air resistance), the velocity-time graph would be a straight line with a positive slope. The slope of this line would be approximately 9.8 m/s², representing the acceleration due to gravity. The line starts at zero (or an initial velocity) and continues to increase linearly with time.

42. How can you identify the moment of turnaround in a round trip journey on a distance-time graph?

On a distance-time graph, the moment of turnaround in a round trip journey is represented by a peak or trough in the curve. At this point, the slope of the tangent line is zero, indicating momentary zero velocity as the object changes direction.

43. What does a velocity-time graph look like for an object moving with constant acceleration?

For an object moving with constant acceleration, the velocity-time graph is a straight line with a non-zero slope. The slope of this line represents the constant acceleration. If the acceleration is positive, the line slopes upward; if negative, it slopes downward.

44. How can you determine if two objects will collide using their distance-time graphs?

To determine if two objects will collide using their distance-time graphs, look for an intersection point between their respective curves. If such a point exists, it indicates that both objects will be at the same position at the same time, signifying a collision. If the curves don't intersect, no collision will occur.

45. What does a looped curve on a distance-time graph represent?

A looped curve on a distance-time graph is physically impossible and represents an error in graphing. Distance is a scalar quantity that can only increase or remain constant with time

46. How can you use a velocity-time graph to determine when an object is farthest from its starting point?

To determine when an object is farthest from its starting point using a velocity-time graph, look for the point where the area under the curve (representing displacement) is at its maximum positive value or minimum negative value. This occurs when the velocity changes from positive to negative or vice versa, crossing the time axis.

47. What does a velocity-time graph look like for an object moving in a circle at constant speed?

For an object moving in a circle at constant speed, the velocity-time graph would be a sinusoidal curve. This is because the velocity vector is constantly changing direction (though not magnitude), resulting in a periodic variation of its components. The graph would oscillate between positive and negative values, representing the changing direction of motion.

48. How can you determine the acceleration at any point on a curved velocity-time graph?

To determine the acceleration at any point on a curved velocity-time graph, find the slope of the tangent line to the curve at that point. This slope represents the instantaneous rate of change of velocity, which is the definition of acceleration.

49. What does a distance-time graph look like for an object moving with constant acceleration?

For an object moving with constant acceleration, the distance-time graph is a parabola. The curve starts with zero slope if the initial velocity is zero, or with a non-zero slope if there's an initial velocity. The parabola opens upward for positive acceleration and downward for negative acceleration (in the direction of motion).

50. How can you use a velocity-time graph to determine the direction of motion at any given time?

On a velocity-time graph, the direction of motion at any given time is indicated by the sign of the velocity. Positive velocity values (above the time axis) indicate motion in the positive direction, while negative values (below the time axis) indicate motion in the negative direction. When the graph crosses the time axis, the object momentarily stops and changes direction.

51. What does a sawtooth pattern on a distance-time graph represent?

A sawtooth pattern on a distance-time graph represents repetitive motion where an object moves in one direction for a period, then quickly returns to its starting position. This could represent scenarios like a piston in an engine or a pendulum with negligible return time. The sharp peaks indicate very rapid returns to the starting position.

52. How can you determine the time spent at rest from a velocity-time graph?

On a velocity-time graph, the time spent at rest is represented by segments of the line that coincide with the time axis. To determine the total time spent at rest, sum up the lengths of all these segments along the time axis.

53. What does a distance-time graph look like for an object moving with constant speed in a circular path?

For an object moving with constant speed in a circular path, the distance-time graph would be a straight line with a positive slope. This is because the distance traveled along the circular path increases linearly with time, even though the displacement (straight-line distance from the starting point) would vary cyclically.

54. How can you use a velocity-time graph to determine the displacement between any two points in time?

To determine the displacement between any two points in time using a velocity-time graph, calculate the area under the velocity curve between those two time points. This area represents the net displacement, taking into account both positive and negative velocities (areas above and below the time axis).

55. What does a velocity-time graph look like for an object thrown vertically upward and then falling back down?

For an object thrown vertically upward and then falling back down, the velocity-time graph would be a straight line with a negative slope. It starts at a positive velocity (upward motion), decreases linearly due to gravity, passes through zero at the highest point, and continues to decrease into negative values as the object falls back down.

56. How can you determine if an object's speed is increasing or decreasing from a distance-time graph?

On a distance-time graph, increasing speed is indicated by an increasing slope (curve becoming steeper), while decreasing speed is shown by a decreasing slope (curve becoming less steep). For a curved line, compare the steepness at different points; for a straight line, the speed is constant.

57. What does a velocity-time graph look like for an object experiencing air resistance while falling?

For an object experiencing air resistance while falling, the velocity-time graph would start as a curved line with a decreasing positive slope. The velocity increases rapidly at first, then the rate of increase slows down as air resistance becomes more significant. Eventually, the graph approaches a horizontal asymptote representing the terminal velocity.

58. How can you use a distance-time graph to determine the instantaneous velocity at any point?

To determine the instantaneous velocity at any point on a distance-time graph, draw a tangent line to the curve at that point. The slope of this tangent line represents the instantaneous velocity at that moment. For a straight-line graph, the instantaneous velocity is constant and equal to the slope of the line.

59. What does a velocity-time graph look like for an object moving with uniformly varying acceleration?

For an object moving with uniformly varying acceleration (jerk), the velocity-time graph would be a parabola. The changing slope of the parabola reflects the continuously changing acceleration. The parabola opens upward if the jerk is positive (acceleration increasing) and downward if the jerk is negative (acceleration decreasing).

60. How can you determine the average acceleration between any two points on a velocity-time graph?

To determine the average acceleration between any two points on a velocity-time graph, calculate the slope of the line connecting these two points. This slope represents the rate of change of velocity with respect to time, which is the definition of average acceleration over that interval.