Pick the correct statements : (a) Average speed of a particle in a given time is never less than the magnitude of the average velocity.

(a) Average speed of a particle in a given time is never less than the magnitude of the average velocity. 

(b) It is possible to have a situation in which |vector dv/dt| ≠ 0 but d/dt|vector v| = 0. 

(c) The average velocity of a particle is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval.

Explanation:   

Since the distance covered by a particle in a given time will never be less than the magnitude of displacement, so average speed is never less than the magnitude of the average velocity. (a) is correct.  

|dv/dt| is the magnitude of the acceleration and d|v|/dt is the rate of change of speed. Consider the case of uniform circular motion. Here speed of the particle is constant, so d|v|/dt=0. But magnitude of the acceleration |dv/dt| ≠ 0. (b) is also correct.  

As we have seen in question no 1, the average velocity of the tip of the minute hand is zero in the time interval of one hour, but its instantaneous velocity is never zero in this interval. So (c) is also correct. 

If average velocity of a particle moving on a straight line is zero in a time interval, it means its displacement is zero. It can only be possible if the particle has returned back to its original position at least once in this time interval. So at the instant when it reverses the direction of its velocity, the instantaneous velocity of the particle will definitely be zero. So (d) is incorrect.

(a) Average speed of a particle in a given time is never less than the magnitude of the average velocity. 

(b) It is possible to have a situation in which |vector dv/dt| ≠ 0 but d/dt|vector v| = 0. 

(c) The average velocity of a particle is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval.

Explanation:   

Since the distance covered by a particle in a given time will never be less than the magnitude of displacement, so average speed is never less than the magnitude of the average velocity. (a) is correct.  

|dv/dt| is the magnitude of the acceleration and d|v|/dt is the rate of change of speed. Consider the case of uniform circular motion. Here speed of the particle is constant, so d|v|/dt=0. But magnitude of the acceleration |dv/dt| ≠ 0. (b) is also correct.  

As we have seen in question no 1, the average velocity of the tip of the minute hand is zero in the time interval of one hour, but its instantaneous velocity is never zero in this interval. So (c) is also correct. 

If average velocity of a particle moving on a straight line is zero in a time interval, it means its displacement is zero. It can only be possible if the particle has returned back to its original position at least once in this time interval. So at the instant when it reverses the direction of its velocity, the instantaneous velocity of the particle will definitely be zero. So (d) is incorrect.