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Uniformly Accelerated Motion - Constant Acceleration, Uniform Acceleration

Uniformly Accelerated Motion - Constant Acceleration, Uniform Acceleration

Vishal kumarUpdated on 02 Jul 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

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

Also read -

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

  1. 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

  1. First equation of motion
    Vf = v0+ at
  1. Second equation of motion
    ∆x =vo t + ½ at2
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  1. Third equation of motion
    ∆x = ½ ( vf + vo) t
  1. Fourth equation of motion
    ∆x = vf t - ½ at 2
  1. 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,

Commonly Asked Questions

Q: What is uniformly accelerated motion?
A:
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.
Q: Why does a free-falling object experience uniformly accelerated motion?
A:
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.
Q: Can an object have constant acceleration if it's slowing down?
A:
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.
Q: What is the relationship between displacement, velocity, and acceleration in uniformly accelerated motion?
A:
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.
Q: How does the slope of a velocity-time graph relate to acceleration in uniformly accelerated motion?
A:
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.

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:

Commonly Asked Questions

Q: How does constant acceleration differ from uniform velocity?
A:
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.
Q: How does air resistance affect uniformly accelerated motion?
A:
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.
Q: Can an object have constant acceleration if it's moving in a circle?
A:
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.
Q: What is the significance of the area under a velocity-time graph in uniformly accelerated motion?
A:
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.
Q: How does the initial velocity affect the motion of an object under constant acceleration?
A:
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.

Frequently Asked Questions (FAQs)

Q: Can an object in uniformly accelerated motion have a constant kinetic energy?
A:
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
Q: What is the significance of the acceleration vector in uniformly accelerated motion?
A:
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.
Q: How does air drag affect the assumption of uniformly accelerated motion for falling objects?
A:
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.
Q: Can an object in uniformly accelerated motion have a changing acceleration vector?
A:
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.
Q: How does the concept of uniformly accelerated motion apply to the motion of planets around the sun?
A:
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.
Q: What is the importance of initial conditions in solving uniformly accelerated motion problems?
A:
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.
Q: How does the concept of uniformly accelerated motion apply to the design of roller coasters?
A:
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.
Q: What is the relationship between uniformly accelerated motion and Newton's First Law of Motion?
A:
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).
Q: How does the concept of uniformly accelerated motion help in understanding projectile motion?
A:
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.
Q: How does the concept of uniformly accelerated motion apply to elevators?
A:
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.
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