Introduction

The concept of motion is related to the change in the position of an object when measured from a fixed point of reference. You would be surprised to know that everything in this world is constantly moving, even if it appears stationary. This is because the Earth itself revolves around the sun. At the same time, there is also motion in this world you can see. Examples of this include vehicles, trains, airplanes, etc. In summer, your ceiling fan spins to propel air toward you, which is also a type of motion. And everything related to motion can be understood in terms of the velocity and acceleration of the object in question. Let us discuss the latter in detail.

What is acceleration?

Acceleration is a vector quantity that measures the rate of change of velocity of an object with respect to time. That is,

Suppose that an object was moving in a straight line and its velocity changed from u to v. If v exceeds u, it means the object must have sped up and the acceleration will turn out to be positive. It is also possible for the object to slow down, leading to a smaller v and thus, a negative value of acceleration. This is known as retardation. When there is no change in the velocity of the object, it is said to have zero acceleration.

When an object is moving randomly, its velocity changes at every instant, and its motion is termed acceleration motion. Sometimes, the amount by which the velocity changes each second remains constant, giving rise to a constant acceleration. The motion of this type is said to be uniformly accelerated. On the other hand, non-uniform acceleration leads to non-uniform changes in velocity.

Unit and Dimensional Formula

The SI unit for acceleration is ms-2. This can be easily derived from its formula since velocity is measured in ms-1 and acceleration is velocity divided by time. Other units for acceleration include km h-2.

The measurement of physical quantities also involves a dimensional analysis, which specifies the basic physical quantities that can be used to specify it. For acceleration. The dimensional expression is [M0LT-2]

Types of Acceleration

1. Average Acceleration

Over time, the value of acceleration may not remain constant at every interval. However, across the whole journey, the average value of the acceleration can be found by taking the difference in the final and initial velocities and dividing them by the time taken. That is,

2. Instantaneous Acceleration

The value of the acceleration of an object at a particular instant in time is known as instantaneous acceleration. It is obtained by taking the limiting case of the formula for acceleration. That is,

3. Centripetal acceleration

When an object tied to a string is whirled around, it moves in a circular path. In such a case, even though its speed does not change, the direction of its velocity changes at every instant in time and thus, an object in circular motion is in accelerated motion.

The acceleration responsible for keeping objects on a circular path acts towards the center of the circle and is known as centripetal acceleration. It is given by:

Centripetal Acceleration

4. Gravitational Acceleration

The acceleration experienced by an object due to gravitational pull is known as gravitational acceleration. We know from experience that all objects fall toward the Earth. This is due to the force of gravity, which all objects in this universe exert on other objects.

On Earth, the acceleration due to gravity has an average value of 9.8 ms⁻². This value does not depend on the mass of the object experiencing acceleration, but it does change from place to place depending on altitude. Interestingly, since acceleration due to gravity does not vary with the mass of the object, a piece of feather and a very heavy brick would fall at the same speed in the absence of external factors like air resistance and friction.

Solved Examples

1. If a car increases its velocity from 10 m/s to 50 m/s in 10 s, find its acceleration.

We know that the formula for acceleration 

Thus, the car has an acceleration of 4 ms⁻², which means that its velocity increases by 4 m/s every second.

2. A car of mass 900 kg moves around a circle of radius 25m with a constant speed of 10 m/s. Calculate the acceleration of the car. 

As previously mentioned, motion in a circular path is accelerated. The centripetal acceleration experienced by the object keeps it on the circular path and this is given by:

Hence, the car is experiencing a centripetal acceleration of 4 ms⁻², which acts toward the center of the circle.

Summary

Acceleration is a physical quantity that measures the change in an object’s velocity with respect to time. It is a vector quantity and its direction is along the direction of the force causing the acceleration.

Acceleration can be classified into several types depending on whether they are constant or varying and even based on their cause. Interestingly, since an object in circular motion constantly changes the direction of its velocity, circular motion is accelerated motion. That is, an object is said to be accelerated even if only the direction of its velocity is changing. The acceleration experienced by objects due to the gravity of the earth is known as acceleration due to gravity and it is approximately given by  g = 9.8 ms-2

Frequently Asked Questions 

1. Can an object have zero velocity and finite acceleration?

Yes. It is possible for the instantaneous values of acceleration and velocity to be non-zero and zero, respectively. For instance, when an object is thrown upwards, then at its peak, it is experiencing an acceleration of 9.8 ms⁻², but its velocity is zero.

2. What is torque?

Torque is a measure of the force applied at a distance and it is also said to be the moment of force. Mathematically, torque is given by the cross-product of force and the distance of the point of application from the axis of rotation.

3. What is Kinetic Energy? 

Kinetic energy is energy related to the motion of an object. An object moving with a certain velocity carries kinetic energy given by

 .

4. Define angular momentum

Angular momentum performs the same task during rotational motion as linear momentum does in linear motion. It is related to the effect of the circular motion of an object.

5. What is average velocity?

The difference in the final and initial displacements of an object with the time taken across the whole journey is known as average velocity.