Motion In A Straight Line - Definition, Formulas, Examples, FAQs

Edited By Vishal kumar | Updated on Jul 02, 2025 04:42 PM IST

In straight motion, an object’s position continuously changes with time and goes in a linear direction relative to a fixed point. The analysis of this type of motion is done using linear kinematics and therefore forces us to introduce concepts such as displacement, velocity, and acceleration, which are all essential in the branch of physics known as kinematics.

Motion In A Straight Line - Definition, Formulas, Examples, FAQs

What is Motion?

Before we begin Motion in a Straight Line motion, let's first introduce 'what is motion'?. In our daily life, we are surrounded by moving objects. For example: Walking on the streets, a running boy, etc. The above movements of the objects are examples of motion.

Motion: The change in the position of any object with respect to time is called motion.
Kinematics: The study of the motion of an object without knowing its cause is called kinematics.

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What is Straight-Line Motion?

Movement is a phenomenon in which an object over time changes position. In terms of movement, distance, speed, acceleration along with time, motion is described quantitatively. In the field of physics that describes the motion of objects but does not refer to the source of objects is called kinematics.

Motion in Straight Line Formulas

Three motions in straight-line formulas are as follows:

1. $\mathrm{v}=\mathrm{u}+\mathrm{at}$
2. $s=u t+0.5 a t^2$
3. $v^2=u^2+2 a s$

Define Linear Motion

Linear motion is the motion that is natural to an object: moving in a straight line. According to Newton's First Law of Motion, an object not affected by any force will continue indefinitely in a straight line. The position x, which varies with t, can be used to explain the motion of a particle (a point-like object) down a line (time). An athlete running 100 metres on a straight track is an example of linear motion. Motion along a straight line is called linear motion.

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Types of Linear Motion

Linear motion, also called Rectilinear Motion can be of two types:
1. Uniform linear motion with constant velocity or zero acceleration
2. Non-uniform linear motion with variable velocity or non-zero acceleration

Movement in a straight line is literally one-dimensional and is simplest. Based on the first law of Newton, this says that an object will remain at rest or continue in straight motion at a uniform speed until an external force does not act upon it.

Do not confuse linear motion with general motion, because as we've mentioned, linear motion is one-dimensional. But in general, it has both a magnitude and direction, such that we describe an object's position and velocity in vector quantities.

Uniform Motion in a Straight Line

if a body moves along a straight path and at regular intervals of time it travels equal distances, it is said to have uniform motion. Simply put, uniform acceleration in the body means that the rate of change of velocity is constant.

Example:
If a car travels at a speed of $60 \mathrm{~km} / \mathrm{hour}$, it will cover a $1 \mathrm{~km} /$ minute. In this sense, the motion of car acceleration is uniform.

Non-uniform Motion in a Straight Line

In contrast to uniform acceleration, a body is said to exhibit non-uniform motion when it has unequal changes in velocity over equal intervals of time - that is, the rate of change of velocity differs at different time points during its motion.

Example:
A boy is kicking a football. It might cover 4 meters in the first attempt, 6 meters in the second change, 9 meters in the third attempt and so on as per the velocity exerted by the boy.

Frequently Asked Questions (FAQs)

1. Give an example of linear motion.

Linear motion is a one-dimensional motion along a straight line. When an object travels in a straight line, its position changes with the passage of time. A stone falling from a set height, an athlete running 200 metres on a straight track, a train travelling on a straight track, along with an automobile going at a consistent speed are all examples of linear motion.

2. What is the definition of motion in a straight line?

The movement of any object from one position to another position with respect to the observer is called Motion and when an object moves along a straight line, the motion of the object is called rectilinear motion.

3. In a straight line motion, what is positive and negative acceleration?

Positive acceleration occurs when an object's speed rises over time. Acceleration is measured in the direction of motion, and it is negative if the speed of an item decreases over time. The direction of motion is reversed with acceleration.

4. What do you mean by motion in one direction?

A particle is considered to be travelling in one dimension if it moves in only one direction throughout its journey.

5. How is displacement different from distance?

Displacement is the shortest straight-line distance between an object's initial and final positions, including direction. Distance is the total length of the path traveled by an object, regardless of direction. For example, if you walk 3 km east and then 3 km west, your total distance is 6 km, but your displacement is 0 km.

6. Can an object have zero displacement but non-zero distance?

Yes, this is possible. If an object moves and returns to its starting point, its displacement is zero because it hasn't changed its position relative to the starting point. However, the total distance traveled would be non-zero because the object has moved along a path.

7. Can an object have zero velocity but non-zero acceleration?

Yes, this is possible at an instant in time. For example, when you throw a ball straight up, at the highest point, its velocity is momentarily zero, but it still has acceleration due to gravity pulling it back down.

8. What's the difference between speed and velocity?

Speed is a scalar quantity that measures how fast an object is moving, regardless of direction. Velocity is a vector quantity that includes both speed and direction. For example, 60 km/h is a speed, while 60 km/h north is a velocity.

9. What is acceleration in the context of linear motion?

Acceleration is the rate of change of velocity with respect to time. In linear motion, it represents how quickly an object's speed or direction is changing. Positive acceleration means the object is speeding up, while negative acceleration (deceleration) means it's slowing down.

10. How is average velocity calculated?

Average velocity is calculated by dividing the displacement (change in position) by the time taken. It's important to note that this uses displacement, not distance, so the average velocity can be different from the average speed if the motion isn't in a straight line.

11. What's the difference between average speed and instantaneous speed?

Average speed is the total distance traveled divided by the total time taken, giving an overall measure of speed for the entire journey. Instantaneous speed is the speed at a specific moment in time, which can be different from the average speed.

12. What does a position-time graph tell us about motion?

A position-time graph shows how an object's position changes over time. The slope of this graph at any point represents the instantaneous velocity. A straight line indicates constant velocity, while a curved line indicates changing velocity (acceleration or deceleration).

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

On a velocity-time graph, acceleration is represented by the slope of the line. If the line is straight and not horizontal, the object is accelerating at a constant rate. If the line is curved, the acceleration is changing. A horizontal line indicates zero acceleration (constant velocity).

14. What is the significance of the area under a velocity-time graph?

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 is exactly what the area under this graph represents.

15. What is motion in a straight line?

Motion in a straight line, also called rectilinear motion, is the movement of an object along a straight path. The object's position changes with time, but its direction remains constant. This type of motion is the simplest form of movement and forms the foundation for understanding more complex motions.

16. How does Newton's First Law relate to motion in a straight line?

Newton's First Law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. This law explains why objects in motion tend to continue moving in a straight line unless something causes them to change direction or speed.

17. What is the difference between uniform motion and non-uniform motion?

Uniform motion occurs when an object travels equal distances in equal intervals of time, meaning it has constant velocity and zero acceleration. Non-uniform motion involves changing velocity, where the object may speed up, slow down, or change direction.

18. Can an object have zero acceleration but non-zero velocity?

Yes, this occurs when an object is moving at a constant velocity. The object has a non-zero speed in a constant direction, but its velocity is not changing, so its acceleration is zero. This is an example of uniform motion.

19. How does the concept of relative motion apply to motion in a straight line?

Relative motion refers to the motion of an object as observed from a particular frame of reference. In straight-line motion, the velocity of an object can appear different to observers in different reference frames. For example, a person walking forward in a train moving in the same direction will appear to have a higher velocity to a stationary observer outside the train than to someone inside the train.

20. How can an object have constant speed but changing velocity?

This occurs when an object moves at a constant rate but changes direction. For example, a car moving around a circular track at a constant speed has a changing velocity because its direction is continuously changing, even though its speed remains the same.

21. How does air resistance affect an object's motion in real-world scenarios?

Air resistance is a force that opposes the motion of objects through air. It increases with speed and can cause objects to reach a terminal velocity where the air resistance balances the force causing the motion (like gravity for a falling object). This means that in real-world scenarios, objects often don't follow the idealized equations of motion that ignore air resistance.

22. What is the significance of the time of flight in projectile motion?

Time of flight in projectile motion is the total time an object spends in the air from launch to landing. It's significant because it determines how long the projectile is subject to gravitational acceleration and helps in calculating the range and maximum height of the projectile. For straight-line vertical motion, it's the time taken for an object to go up and come back down to its original height.

23. How does the principle of independence of motions apply to projectile motion?

The principle of independence of motions states that in projectile motion, the horizontal and vertical components of motion are independent of each other. This means that the horizontal motion continues with constant velocity (neglecting air resistance), while the vertical motion is subject to gravitational acceleration. This principle allows us to analyze complex projectile motions by treating the horizontal and vertical components separately.

24. What is the significance of initial velocity in projectile motion?

Initial velocity in projectile motion determines both the range and height of the projectile's path. Its magnitude affects how far and how high the projectile will go, while its direction (angle) determines the shape of the trajectory. Understanding the role of initial velocity is crucial for predicting and analyzing the motion of projectiles.

25. Can an object have a negative acceleration but still be speeding up?

Yes, this can happen if the object is moving in the negative direction (opposite to the chosen positive direction) and speeding up. For example, if we define the positive direction as upward, an object falling faster and faster would have negative acceleration but be speeding up.

26. What is the equation for displacement in uniformly accelerated motion?

The equation for displacement (s) in uniformly accelerated motion is: s = ut + (1/2)at², where u is the initial velocity, t is time, and a is acceleration. This equation allows you to calculate displacement without needing to know the final velocity.

27. What is the physical meaning of the slope of a distance-time graph?

The slope of a distance-time graph represents the speed of the object. A steeper slope indicates higher speed, while a flatter slope indicates lower speed. A horizontal line means the object is stationary, and a curved line indicates changing speed.

28. What is the significance of the sign (positive or negative) in velocity and acceleration?

The sign of velocity and acceleration indicates direction relative to a chosen coordinate system. Positive usually means motion or acceleration in the direction defined as positive, while negative means the opposite. For example, if we define rightward as positive, then leftward velocity and acceleration would be negative.

29. How do initial conditions affect the motion of an object?

Initial conditions, such as initial position and initial velocity, are crucial in determining an object's subsequent motion. They serve as the starting point for all calculations and predictions about the object's future positions and velocities. Different initial conditions can lead to vastly different motion outcomes, even under the same forces or accelerations.

30. What is meant by 'equations of motion' in the context of straight-line motion?

Equations of motion are mathematical relationships that describe the motion of objects. For straight-line motion with constant acceleration, there are three main equations:

31. How does the concept of instantaneous quantities differ from average quantities in motion?

Instantaneous quantities (like instantaneous velocity or acceleration) describe the state of motion at a specific moment in time, while average quantities describe the overall behavior over a period of time. Instantaneous quantities are represented by the slope of the tangent line on a graph at a point, while average quantities are represented by the slope of the secant line between two points.

32. What is the physical interpretation of the area under an acceleration-time graph?

The area under an acceleration-time graph represents the change in velocity over that time period. This is because acceleration is the rate of change of velocity with respect to time, so integrating acceleration (finding the area under its graph) gives the total change in velocity.

33. How does the principle of superposition apply to motion in a straight line?

The principle of superposition states that when multiple forces act on an object, their combined effect is the sum of the effects of each force acting individually. In straight-line motion, this means that if an object is subject to multiple accelerations, its total acceleration is the vector sum of all individual accelerations.

34. What is the difference between average acceleration and instantaneous acceleration?

Average acceleration is the change in velocity divided by the time interval over which this change occurs. It gives an overall measure of acceleration for a period of time. Instantaneous acceleration is the acceleration at a specific moment in time, calculated as the limit of average acceleration as the time interval approaches zero.

35. How does gravity affect motion in a straight line on Earth's surface?

On Earth's surface, gravity causes a constant downward acceleration of approximately 9.8 m/s² (neglecting air resistance). This affects vertical motion, causing objects thrown upward to slow down and eventually fall back down, and objects dropped or thrown downward to accelerate. For horizontal motion, gravity doesn't directly affect the horizontal component of velocity but influences the path of projectiles.

36. What is the relationship between displacement, velocity, and acceleration in straight-line motion?

In straight-line motion, velocity is the rate of change of displacement with respect to time, and acceleration is the rate of change of velocity with respect to time. Mathematically, velocity is the first derivative of displacement with respect to time, and acceleration is the second derivative of displacement or the first derivative of velocity with respect to time.

37. How does the concept of frames of reference apply to motion in a straight line?

A frame of reference is a coordinate system from which motion is observed. The description of an object's motion can change depending on the chosen frame of reference. For example, a person walking forward in a moving train appears stationary relative to the train (train's frame of reference) but moving relative to the ground (Earth's frame of reference).

38. How does the concept of free fall relate to motion in a straight line?

Free fall is a special case of straight-line motion where an object moves under the influence of gravity alone, neglecting air resistance. In free fall, objects accelerate downward at approximately 9.8 m/s² near Earth's surface. This results in a straight-line motion with constant acceleration, making it a perfect example for applying the equations of motion.

39. What is the difference between scalar and vector quantities in the context of linear motion?

In linear motion, scalar quantities (like speed and distance) have only magnitude, while vector quantities (like velocity and displacement) have both magnitude and direction. For example, traveling 50 km/h is a scalar speed, while moving 50 km/h north is a vector velocity. Understanding this distinction is crucial for correctly analyzing and solving motion problems.

40. How does the concept of relative velocity apply to motion in a straight line?

Relative velocity is the velocity of an object as observed from another moving object or frame of reference. In straight-line motion, if two objects are moving along the same line, their relative velocity is the difference between their individual velocities. This concept is important for understanding how motion appears from different perspectives and for solving problems involving multiple moving objects.

41. What is meant by 'kinematics' in the study of motion in a straight line?

Kinematics is the branch of physics that describes the motion of objects without considering the forces that cause the motion. In the context of straight-line motion, kinematics involves studying and describing how position, velocity, and acceleration change over time, often using graphs and equations of motion.

42. How does the concept of inertia relate to motion in a straight line?

Inertia is the resistance of an object to any change in its motion. In straight-line motion, inertia explains why objects tend to maintain their state of motion (either at rest or moving with constant velocity) unless acted upon by an external force. This principle is fundamental to understanding why objects continue moving in a straight line when no forces are acting on them.

43. What is the physical meaning of the area under a speed-time graph?

The area under a speed-time graph represents the distance traveled by the object. This is because distance is the product of speed and time, which is exactly what the area under this graph represents. For non-uniform motion, the total distance can be found by calculating the area under the entire curve.

44. How does air resistance affect the equations of motion for straight-line motion?

Air resistance introduces a force that opposes motion and typically increases with speed. This makes the equations of motion more complex, as acceleration is no longer constant. With air resistance, objects tend to reach a terminal velocity where the air resistance force balances the driving force (like gravity for falling objects). This results in motion that deviates from the simple equations used for motion in a vacuum.

45. What is the relationship between average velocity and instantaneous velocity?

Average velocity is the displacement divided by the time interval for a given period, while instantaneous velocity is the velocity at a specific moment in time. Instantaneous velocity can be thought of as the limit of average velocity as the time interval approaches zero. In a velocity-time graph, average velocity is represented by the slope of the secant line, while instantaneous velocity is the slope of the tangent line at a point.

46. How does the concept of momentum relate to motion in a straight line?

Momentum is the product of an object's mass and velocity. In straight-line motion, momentum is a vector quantity pointing in the direction of motion. The concept of momentum is important because it is conserved in collisions and interactions, providing a powerful tool for analyzing complex motions and predicting outcomes of interactions between objects.

47. What is the significance of the acceleration due to gravity (g) in vertical motion problems?

The acceleration due to gravity (g), approximately 9.8 m/s² near Earth's surface, is crucial in vertical motion problems. It represents the constant acceleration experienced by objects in free fall or vertical projectile motion (neglecting air resistance). This constant acceleration allows us to use the equations of motion to predict the position and velocity of objects at different times during their vertical motion.

48. How does the concept of work relate to motion in a straight line?

Work is done when a force acts on an object and causes a displacement in the direction of the force. In straight-line motion, work is calculated as the product of the force and the displacement in the direction of the force. Understanding work is important because it relates to energy transfer and can help in analyzing the causes and effects of motion.

49. What is the difference between distance and displacement in circular motion compared to linear motion?

In linear motion, distance and displacement can be equal if the motion is in one direction. However, in circular motion, they are always different. The distance traveled in circular motion is the length of the arc, while the displacement is the straight-line distance between the start and end points. After one complete revolution in circular motion, the distance traveled is the circumference of the circle, but the displacement is zero.

50. How does the concept of centripetal acceleration relate to linear motion?

Centripetal acceleration is the acceleration directed towards the center of a circular path, causing an object to move in a circle. While it's not directly part of linear motion, understanding centripetal acceleration helps explain why objects don't continue in a straight line when moving in a circle. It's the presence of this acceleration that causes deviation from straight-line motion.

51. What is the role of friction in real-world linear motion scenarios?

Friction is a force that opposes the relative motion of objects in contact. In real-world linear motion, friction can cause objects to slow down (like a car braking) or prevent motion altogether (static friction). Friction complicates the equations of motion because it introduces a force that depends on the nature of the surfaces in contact and the normal force between them. Understanding friction is crucial for accurately predicting and analyzing motion in practical situations.