Chapter 5, Problem 12Q

To determine

To explain:

Whether a particle with constant speed be accelerating, and if it has a constant velocity.

Answer to Problem 12Q

Solution:

Acceleration is defined as the rate of change of velocity. Velocity has magnitude as well as direction.Accelerationcan be produced by either changing magnitude or direction or both.

A particle with a constant speed canaccelerate by changing direction only.

A particle with constant velocity can’t accelerate because constant velocity means zero acceleration.

Explanation of Solution

Constant speed means the magnitude of velocity is not changing but the direction may change. Example: A uniform circular motion hasa constantspeed, but direction continuously changes, and it has centripetal acceleration $\left(a_n\right)=\frac{v^2}{r}$ due to change in direction.

Hence, a particle with a constant speed can have acceleration, but a particle that has constant velocity can’t have acceleration.

Conclusion:

A particle with a constant speed can have acceleration, but a particle with constant velocity can’t have acceleration.