Uniformly Accelerated Motion - Constant Acceleration, Uniform Acceleration

Edited By Vishal kumar | Updated on Jul 02, 2025 05:07 PM IST

In this article we are going to study a very important topic of class 9. We will go through to this topic by covering the given topics one by one. In uniformly accelerated motion we will see what is uniform acceleration that is uniform acceleration definition, example of uniform acceleration, what is constant acceleration, equation of uniformly accelerated motion, difference between uniform acceleration and non-uniform acceleration, constant accelerated motion and its formula.

Uniformly Accelerated Motion - Constant Acceleration, Uniform Acceleration

uniformly accelerated motion

First let’s revise,

What is acceleration?

Rate of change of velocity with respect to time is known as acceleration.

Any person who is speeding up, speeding down, or changing its direction while moving is accelerating. This means that acceleration is associated with change in speed or in direction or both of them.

A = dv / dt here a is representing acceleration

V is velocity and t is time

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What is uniform acceleration / uniformly acceleration definition

If a vehicle maintains a constant or a uniform change in its velocity in a given time interval along a straight line then the vehicle is said to have a constant acceleration and its motion is defined as uniformly accelerated motion.

Diagram of moving car

Uniformly accelerated motion is the motion of an object in which acceleration through out the motion is uniform. So acceleration w is constant. In the case of uniformly accelerated rectilinear motion, the object moves with uniform speed with zero acceleration.

Example of uniform acceleration

There can be various examples of uniformly accelerated motion are :

1. Motion of a ball dropped from a height a body moving with a constant speed in a straight line has a uniform motion.

ball dropped

2. Motion of a bicycle going down the slope of a road when the rider is not paddling and the wind resistance is negligible .

3. A freely falling body is also an example of uniformly accelerated motion.

A group of people jumping into the water free fall

Motion of earth around the sun and many more.

Equation of uniformly accelerated motion

Kinematics equation for uniformly accelerated motion

a = the acceleration taken to be constant,

t = time the object has been accelerating,

v0 = initial velocity of the GIVEN object,

vf = FINAL velocity of the object at time t ,

∆x = displacement of the object during the time interval.

graphical method

First equation of motion
Vf = v0+ at

Second equation of motion
∆x =vo t + ½ at2

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Third equation of motion
∆x = ½ ( vf + vo) t

Fourth equation of motion
∆x = vf t - ½ at 2

Fifth equation of motion
vf 2 = vo 2 + 2 a ∆x.

These are the equations used for calculating the various components like initial velocity, final velocity, acceleration, time or distance. These equations are derived by using graphical method.

Related Topics Link,

Difference between uniform and non-uniform motion

Uniform accelerated motion

Defining the term ,uniform acceleration motion implies the movement of a body along a straight line with an increase in its velocity by equal interval of time.
Some example of uniformly accelerated motion is the motion of a freely falling body, a bicycle going down the slope of a road, a ball falling from the top of the building.

A person riding a bike

Non-uniform accelerated motion

Non-uniform accelerated motion is the one in which acceleration is not uniform. An example of non uniformly accelerated motion is a car running on a crowded city road. It changes at one moment when the velocity of car increases.

A red car on road

Also Read:

Constant accelerated motion and its formula.

As now we know that constant accelerated motion is if some object is changing its speed with regular interval of duration.

And formulas used are ;

Writing the three equations of uniformly accelerated motion

Vf = v0+ at

∆x =vo t + ½ at2

∆x = ½ ( vf + vo) t

Now we all have studied,

Also check-

NCERT Physics Notes:

Frequently Asked Questions (FAQs)

1. What are positive and negative acceleration in a straight line?

If velocity of a particle increases with time then its acceleration is said to be positive acceleration whereas if the velocity of a particle keeps on decreasing it is known as negative acceleration or deceleration.

2. Motion in a plane with constant acceleration.

If we take a particle moving in xy coordinate plane with a constant acceleration a located at point b at time t which has a position coordinate r and velocity v. It reaches point b’ has a position coordinate r’ and velocity v’ . Constant acceleration a is equal to change in velocity by time.

3. What is free fall?

Freefall is the downward motion under the influence of gravity in other words when the only force acting on an object is gravity the object is said to be in freefall in vacuum that is in no air all objects in freefall accelerate at the same rate regardless of mass likewise a ball falling down with negligible air resistance. Freefall objects falling unaffected by air resistance owners we can’t fall without air resistance but for normal situation the numbers are realistic when things fall they constantly accelerate if we can ignore air resistance all objects excellent at the same rate that is at the acceleration due to gravity on earth at sea level.

4. Difference between constant acceleration and uniform acceleration .

In constant acceleration the body moving in a particular direction does not change its direction whereas in uniform acceleration the particle covers an equal distance in equal duration of time hence in both the situation acceleration of the body is zero.

5. What is the difference between uniform motion and uniform speed?

Uniform motion meant uniform velocity but uniform speed is change in direction likewise for uniform circular motion hair the speed of the particle remains same but the direction of particle keeps on changing.

6. How does constant acceleration differ from uniform velocity?

Constant acceleration involves a continuous change in velocity over time, while uniform velocity means the speed and direction remain constant. In uniformly accelerated motion, the velocity changes at a steady rate, whereas in uniform velocity, there is no change in speed or direction.

7. How does air resistance affect uniformly accelerated motion?

Air resistance opposes the motion of an object, causing its acceleration to decrease over time. In reality, most objects moving through air do not experience perfectly uniform acceleration due to this resistance. As speed increases, so does air resistance, eventually leading to terminal velocity where acceleration becomes zero.

8. Can an object have constant acceleration if it's moving in a circle?

Yes, an object moving in a circle can have constant acceleration, but it's not uniformly accelerated motion in a straight line. In circular motion, the acceleration is constant in magnitude but continuously changing in direction, always pointing towards the center of the circle. This is called centripetal acceleration.

9. What is the significance of the area under a velocity-time graph in uniformly accelerated motion?

The area under a velocity-time graph represents the displacement of the object. For uniformly accelerated motion, this graph is a straight line (not horizontal), and the area forms a trapezoid. Calculating this area gives the total distance traveled by the object during the time interval.

10. How does the initial velocity affect the motion of an object under constant acceleration?

The initial velocity determines the starting point of the motion and influences the object's position at any given time. If the initial velocity is in the same direction as the acceleration, the object will speed up faster. If it's in the opposite direction, the object will slow down before potentially changing direction, depending on the magnitude and duration of the acceleration.

11. What is uniformly accelerated motion?

Uniformly accelerated motion is a type of motion where an object's velocity changes at a constant rate over time. In this motion, the acceleration remains constant throughout the object's movement, resulting in a steady increase or decrease in speed.

12. Why does a free-falling object experience uniformly accelerated motion?

A free-falling object experiences uniformly accelerated motion due to the constant gravitational force of the Earth. Neglecting air resistance, this force causes the object to accelerate at a constant rate of approximately 9.8 m/s² towards the Earth's center, resulting in uniform acceleration.

13. Can an object have constant acceleration if it's slowing down?

Yes, an object can have constant acceleration while slowing down. This is called negative acceleration or deceleration. The acceleration is still constant, but it opposes the direction of motion, causing the object to slow down at a steady rate.

14. What is the relationship between displacement, velocity, and acceleration in uniformly accelerated motion?

In uniformly accelerated motion, displacement (s) is related to initial velocity (u), time (t), and acceleration (a) by the equation: s = ut + (1/2)at². The velocity (v) at any time is given by v = u + at. These equations show how displacement and velocity change with constant acceleration over time.

15. How does the slope of a velocity-time graph relate to acceleration in uniformly accelerated motion?

In a velocity-time graph for uniformly accelerated motion, the slope of the line represents the acceleration. A positive slope indicates positive acceleration (speeding up), while a negative slope shows negative acceleration (slowing down). The steeper the slope, the greater the magnitude of acceleration.

16. How can you use the concept of uniformly accelerated motion to calculate stopping distances for vehicles?

Stopping distance calculations use uniformly accelerated motion principles. The total stopping distance is the sum of the reaction distance (distance traveled during the driver's reaction time at constant velocity) and the braking distance (distance traveled while decelerating). The braking distance is calculated using the equations of uniformly accelerated motion, assuming constant deceleration.

17. How does the concept of uniformly accelerated motion apply to inclined planes?

On an inclined plane, an object experiences uniformly accelerated motion due to a component of gravity acting parallel to the plane. The acceleration is constant but less than free-fall acceleration, depending on the angle of inclination. The motion can be analyzed using the same equations as for vertical uniformly accelerated motion, but with the adjusted acceleration value.

18. How does uniformly accelerated motion apply to the concept of escape velocity?

Escape velocity is the minimum speed an object needs to escape a planet's gravitational field. While the motion of an object trying to escape is uniformly accelerated (due to constant gravitational acceleration), the concept of escape velocity uses energy considerations. An object with exactly escape velocity will slow down under uniform acceleration, asymptotically approaching zero velocity at infinite distance from the planet.

19. How does the concept of uniformly accelerated motion apply to safety features in vehicles?

Uniformly accelerated motion principles are crucial in designing vehicle safety features. Crumple zones, airbags, and seat belts are all designed to extend the time of deceleration during a collision, effectively reducing the acceleration experienced by occupants. By understanding uniform acceleration, engineers can calculate and optimize the forces involved in vehicle collisions to maximize safety.

20. What is the relationship between uniformly accelerated motion and gravitational potential energy?

In uniformly accelerated motion under gravity, there's a direct relationship between the motion and changes in gravitational potential energy. As an object falls, its gravitational potential energy decreases while its kinetic energy increases. The total mechanical energy remains constant (in the absence of air resistance), demonstrating the principle of energy conservation in uniformly accelerated motion.

21. Why is the acceleration-time graph a horizontal line for uniformly accelerated motion?

The acceleration-time graph for uniformly accelerated motion is a horizontal line because the acceleration remains constant over time. The height of this line from the time axis represents the magnitude of the constant acceleration, and its position above or below the axis indicates whether the acceleration is positive or negative.

22. What is the difference between average velocity and instantaneous velocity in uniformly accelerated motion?

Average velocity is the total displacement divided by the total time taken, while instantaneous velocity is the velocity at a specific moment. In uniformly accelerated motion, the instantaneous velocity changes continuously, while the average velocity represents the overall rate of displacement over a time interval.

23. How can you determine if an object is experiencing uniformly accelerated motion by observing its position?

To determine if an object is experiencing uniformly accelerated motion by observing its position, you would need to measure its position at equal time intervals. If the changes in position follow a quadratic pattern (forming a parabola when graphed against time), it indicates uniform acceleration.

24. Why do objects thrown vertically upward experience uniformly accelerated motion?

Objects thrown vertically upward experience uniformly accelerated motion due to the constant gravitational acceleration of Earth. As the object rises, gravity continuously decelerates it at a constant rate until it stops and begins to fall. During the fall, the same acceleration causes it to speed up at a constant rate.

25. How does mass affect an object's acceleration in uniformly accelerated motion?

In the absence of air resistance, mass does not affect an object's acceleration in uniformly accelerated motion. This is because the gravitational force increases proportionally with mass, canceling out its effect on acceleration. However, in the presence of air resistance or other forces, objects with different masses may accelerate differently.

26. What is the relationship between kinetic energy and uniformly accelerated motion?

In uniformly accelerated motion, an object's kinetic energy changes continuously. The change in kinetic energy is directly related to the work done by the accelerating force. As velocity increases, kinetic energy increases quadratically (KE = 1/2 mv²), demonstrating how small changes in velocity can lead to significant changes in energy.

27. What is the significance of the acceleration due to gravity (g) in uniformly accelerated motion problems?

The acceleration due to gravity (g), approximately 9.8 m/s² near Earth's surface, is a constant acceleration that affects all objects in free fall or projectile motion near Earth. It's used in many uniformly accelerated motion problems involving vertical motion, allowing for calculations of time, velocity, and displacement for objects moving under the influence of gravity.

28. How does uniformly accelerated motion apply to the concept of terminal velocity?

Terminal velocity is reached when an object's acceleration becomes zero due to air resistance balancing the gravitational force. Before reaching terminal velocity, an object in free fall experiences uniformly accelerated motion. As it accelerates, air resistance increases until it equals the gravitational force, resulting in zero net force and constant velocity.

29. Can an object have zero velocity but non-zero acceleration in uniformly accelerated motion?

Yes, an object can have zero velocity but non-zero acceleration in uniformly accelerated motion. This occurs at the moment when an object changes direction, such as at the highest point of a vertical throw. At this instant, the velocity is zero, but the acceleration (due to gravity) remains constant and non-zero.

30. What is the importance of the equation v² = u² + 2as in uniformly accelerated motion?

The equation v² = u² + 2as is crucial in uniformly accelerated motion as it relates final velocity (v) to initial velocity (u), acceleration (a), and displacement (s) without involving time. This makes it particularly useful in problems where time is not given or needed, allowing for direct calculation of velocity changes over a given distance.

31. How does uniformly accelerated motion relate to the concept of jerk in physics?

Jerk is the rate of change of acceleration. In uniformly accelerated motion, the jerk is zero because the acceleration is constant. Any non-zero jerk would indicate that the acceleration is changing, which would no longer be uniform acceleration. Understanding jerk helps in analyzing more complex motions and in designing smooth transportation systems.

32. Can an object have constant speed but non-constant velocity in uniformly accelerated motion?

No, an object cannot have constant speed but non-constant velocity in uniformly accelerated motion. In uniformly accelerated motion, the velocity is constantly changing, which means both the speed (magnitude of velocity) and direction may change. Constant speed with changing direction is uniform circular motion, not uniformly accelerated motion.

33. How does the concept of uniformly accelerated motion apply to elevators?

Elevators experience uniformly accelerated motion during the start and stop of their journey. When an elevator begins to move, it accelerates at a constant rate until it reaches its operating speed. When stopping, it decelerates at a constant rate until it comes to rest. This acceleration and deceleration can be felt by passengers and is carefully controlled for comfort and safety.

34. What is the significance of the time squared term in the displacement equation for uniformly accelerated motion?

The time squared term (1/2 at²) in the displacement equation (s = ut + 1/2 at²) reflects the cumulative effect of acceleration over time. It shows that displacement increases quadratically with time under constant acceleration, not linearly. This term is responsible for the parabolic shape of the position-time graph in uniformly accelerated motion.

35. How does uniformly accelerated motion relate to the concept of momentum?

In uniformly accelerated motion, an object's momentum changes at a constant rate. Since momentum is the product of mass and velocity (p = mv), and velocity is changing uniformly, the rate of change of momentum (which is equal to the force causing the acceleration) is constant. This relationship is expressed in Newton's Second Law: F = ma = dp/dt.

36. Can an object have uniformly accelerated motion if multiple forces are acting on it?

Yes, an object can have uniformly accelerated motion even with multiple forces acting on it, as long as the net force remains constant. If the vector sum of all forces results in a constant net force, the object will experience uniform acceleration in the direction of this net force, regardless of the number or complexity of the individual forces involved.

37. How does the concept of work relate to uniformly accelerated motion?

In uniformly accelerated motion, work is done by the force causing the acceleration. The work-energy theorem states that the work done on an object equals its change in kinetic energy. In uniform acceleration, this work can be calculated using the equation W = F * d, where F is the constant force and d is the displacement. This work directly corresponds to the change in the object's kinetic energy.

38. What is the significance of the average velocity formula in uniformly accelerated motion?

The average velocity formula for uniformly accelerated motion, vavg = (u + v)/2, where u is the initial velocity and v is the final velocity, is significant because it simplifies calculations. It shows that the average velocity is the arithmetic mean of the initial and final velocities, which is true only for uniform acceleration. This formula is useful for calculating displacement when time and acceleration are known.

39. Can an object in uniformly accelerated motion ever come to a complete stop?

Yes, an object in uniformly accelerated motion can come to a complete stop if the acceleration is in the opposite direction to its initial velocity. The time taken to stop can be calculated using the equation v = u + at, setting v to zero and solving for t. After stopping, if the acceleration continues, the object will start moving in the opposite direction.

40. How does uniformly accelerated motion relate to the concept of relative motion?

Uniformly accelerated motion can be observed and analyzed from different reference frames, illustrating the concept of relative motion. For example, an object in free fall appears to have uniformly accelerated motion to an observer on Earth, but to an observer falling alongside the object, it appears stationary. This highlights the importance of specifying the frame of reference when discussing acceleration and motion.

41. What is the significance of the acceleration vector in uniformly accelerated motion?

The acceleration vector in uniformly accelerated motion is crucial as it determines the direction and rate of change of velocity. Its constant magnitude and direction define the motion as uniformly accelerated. The acceleration vector always points in the direction of the velocity change, which may or may not be the same as the direction of motion, depending on whether the object is speeding up, slowing down, or changing direction.

42. How does air drag affect the assumption of uniformly accelerated motion for falling objects?

Air drag complicates the assumption of uniformly accelerated motion for falling objects. As an object falls, air resistance increases with velocity, opposing the motion. This causes the acceleration to decrease over time, deviating from uniform acceleration. Eventually, when air resistance equals the gravitational force, the object reaches terminal velocity and no longer accelerates, moving at a constant speed instead.

43. Can an object in uniformly accelerated motion have a changing acceleration vector?

No, an object in truly uniformly accelerated motion cannot have a changing acceleration vector. By definition, uniform acceleration means the acceleration vector (both magnitude and direction) remains constant throughout the motion. If the acceleration vector changes in any way, either in magnitude or direction, it is no longer considered uniformly accelerated motion.

44. How does the concept of uniformly accelerated motion apply to the motion of planets around the sun?

While planets' motion around the sun is not uniformly accelerated in a straight line, it does involve constant acceleration towards the sun due to gravity. This centripetal acceleration changes the direction of the planet's velocity vector continuously, resulting in elliptical orbits. Understanding uniform acceleration helps in analyzing the components of this complex motion and in deriving Kepler's laws of planetary motion.

45. What is the importance of initial conditions in solving uniformly accelerated motion problems?

Initial conditions, such as initial position and velocity, are crucial in solving uniformly accelerated motion problems. They provide the starting point for all calculations and determine the specific solution to the equations of motion. Different initial conditions can lead to vastly different outcomes even with the same acceleration, highlighting the importance of accurately defining the initial state of the system.

46. How does the concept of uniformly accelerated motion apply to the design of roller coasters?

Roller coaster design extensively uses principles of uniformly accelerated motion. The initial climb and subsequent falls involve sections of nearly uniform acceleration due to gravity. Designers use these principles to calculate velocities, forces, and energy transfers throughout the ride. Understanding uniform acceleration helps in creating thrilling yet safe experiences by controlling the accelerations experienced by riders at different points of the track.

47. What is the relationship between uniformly accelerated motion and Newton's First Law of Motion?

Newton's First Law states that an object remains at rest or in uniform motion unless acted upon by an external force. Uniformly accelerated motion occurs when a constant net force acts on an object, causing it to deviate from the state described by the First Law. The acceleration in uniformly accelerated motion is directly related to this constant net force, as described by Newton's Second Law (F = ma).

48. How does the concept of uniformly accelerated motion help in understanding projectile motion?

Uniformly accelerated motion is key to understanding projectile motion. In projectile motion, the vertical component of the motion is uniformly accelerated due to gravity, while the horizontal component typically has constant velocity (neglecting air resistance). By analyzing these components separately using principles of uniform acceleration, we can predict the path, range, and time of flight of projectiles.

49. Can an object in uniformly accelerated motion have a constant kinetic energy?

No, an object in uniformly accelerated motion cannot have a constant kinetic energy. Since kinetic energy is proportional to the square of velocity (KE = 1/2 mv²), and velocity is constantly changing in uniformly accelerated motion, the kinetic energy must also be