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the Question is as follows:

Pick the correct statement:

(a) The 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 |dv/dt| ≠ 0 but d|v|/dt=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.

(d) The average velocity of a particle moving on a straight line is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval. (Infinite accelerations are not allowed.)

and ans is option (a)(b)(c)

I do understand everything. here is my logic for all options :

Since the distance covered by a particle in a given time will never be less than the magnitude of displacement, so the 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 the 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 the average velocity of a particle moving in 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.

what I don't understand is the significance of the line "(Infinite accelerations are not allowed.)".? has it anything to do with the question? please also correct me if any of the logic is wrong.

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closed as off-topic by G. Smith, John Rennie, Bob D, Jon Custer, ZeroTheHero Sep 17 at 0:30

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  • $\begingroup$ for d) did you think of oscillating on the interval? Infinite acceleration would allow to go from -v to v? (ball on a line bouncing between two walls). $\endgroup$ – anna v Sep 16 at 5:37
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I think you are querying the necessity of the statement

Infinite accelerations are not allowed

To get zero displacement one has to have a positive displacement and a negative displacement and hence at some stage the velocity must be zero as shown on the left hand graph which is continuous and well behaved.

enter image description here

Now what about going from a velocity $v_{\rm A}$ to a velocity $v_{\rm B}$ instantaneously which would require an infinite acceleration.
Possibly the statement Infinite accelerations are not allowed was added by the question setter to quash any debate as to which the velocities are present during the switching of the signs of velocity during an infinite acceleration, eg only $v_{\rm A}$ and $v_{\rm B}$ or including all values between $v_{\rm A}$ and $v_{\rm B}$?

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  • $\begingroup$ Thanks for a clear cut explanation. $\endgroup$ – Garima Singh Sep 16 at 7:49

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