Question

(a) Can the velocity of an object at an instant of time be greater in magnitude than the average velocity over a time interval containing the instant? (b) Can it be less?

Short answer

(a) The velocity of object is greater than average velocity for increasing velocity.

(b) The velocity of object is less than average velocity for decreasing velocity.

Step-by-step solution

Velocity

The variation in the position of the particle with time is called the velocity. If variation is taken at some instant then it is called instantaneous velocity. If variation is considered for a time interval then called average velocity in that time interval.

Possibility for magnitude of velocity greater than average velocity(a)

The velocity of an object at an instant of time can be greater in magnitude than average velocity over a time interval if the position of object at that instant of time is increasing with time.

While a particle moves towards the bottom of the circle in circular motion then instantaneous velocity of the particle at an instant become greater than average velocity of particle.

Therefore, the velocity of object is greater than average velocity for increasing velocity.

Possibility for magnitude of velocity less than average velocity(b)

The velocity of an object at an instant of time can be less in magnitude than average velocity over a time interval if the position of object at that instant of time is decreasing with time.

While a particle moves towards the top of the circle in circular motion then instantaneous velocity of the particle at an instant become less than average velocity of particle.

Therefore, the velocity of object is less than average velocity for decreasing velocity.