Question

The acceleration of a particle changes when

• A. Direction of velocity changes
• B. Magnitude of velocity changes
• C. Both (A) and (B)
• D. Speed changes uniformly

Answer 1

The correct option is C

Both (A) and (B)

Explanation for the correct option:

Option (C):

1. The acceleration of the particle is defined as the rate of change of the velocity to the time.
2. Acceleration is a vector quantity. It changes when both the magnitude and the direction change.
3. Acceleration$=$change in velocity/time
4. Since velocity is a vector quantity so acceleration is also a vector quantity as acceleration is directly proportional to the velocity
5. Vector quantity is the quantity which has both magnitude and direction.

Exceptions:

1. Uniform acceleration: In that case, velocity changes equally in equal intervals of time thus, the acceleration remains constant.
2. Projectile motion: In that case, the direction of velocity changes but acceleration remains the same.
3. Free fall: In this case also the direction of velocity changes but the acceleration remains the same.

Explanation for the incorrect option:

1. The magnitude of the velocity is known as speed, thus, if the speed changes at the non-uniform rate then the acceleration of the body changes as well but if the speed changes at a uniform rate then the acceleration of the body will not change.
2. Therefore, when either of the options (A) or (B) occurs then the acceleration of a particle changes.

Therefore, the acceleration changes with both the magnitude and the direction of the velocity.

Hence, option $\left(C\right)$ is correct.