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I was solving exercises on Physics Part I: Textbook for Class XI, NCERT, ed. July 2021 when I came across the following question:

A particle in one-dimensional motion with constant speed must have zero acceleration

We've got to say if this statement's true or false, with a reason and an example.

When I headed over to the answer section, I found that they've said:

True (if the particle rebounds instantly with the same speed, it implies infinite acceleration which is unphysical)

How does a particle which rebounds instantly with the same speed have infinite acceleration?

archthegreat
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    Have you drawn a graph of velocity vs. time? What is its slope when the particle rebounds? – Ghoster Sep 27 '22 at 19:16
  • This is an example of a physical approximation. Nothing can have infinite acceleration, but we can assume that the acceleration is so high that the time that it takes for the rebound to happen doesn't matter for the remainder of our calculations. Physics, as my old professor put it, is the art of approximation and when it works it's allowed. You are correct, though, that one has to be careful with such approximations. They often work but occasionally they introduce unphysical effects that mess up the result. – FlatterMann Sep 27 '22 at 19:30
  • A rebounding particle does not have zero acceleration, regardless of what NCERT thinks. – Ghoster Sep 27 '22 at 19:30
  • NCERT has an "if" in his sentence, and than "Implies" , and unphysical wich means impossible. – trula Sep 27 '22 at 19:39
  • the answers in this question may help https://physics.stackexchange.com/questions/543805/momentum-conservation-in-ball-and-massive-wall-collision – anna v Sep 28 '22 at 04:20

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If you consider a rebounding particle in 1D, an instantaneous change in velocity (say from +x towards -x direction; but with the magnitude / speed remaining the same) means that the change happens in an instant - the time elapsed during this reversal is zero. Anything divided by zero blows up and as acceleration is defined as change in velocity over some time interval, hence acceleration in the rebounding scenario becomes infinite.

Practically speaking, a force needs to be applied to the particle for rebounding to happen. For the acceleration to be infinite the force must also be infinite (assuming the the particle has non zero mass). Infinities in the world are impossible to attain therefore this scenario is unpractical / unphysical.

You can reframe the question and ask yourself: A particle in one-dimensional motion with constant velocity must have zero acceleration

The answer is always True (with no ifs and buts).

SupremeBeing
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A particle in one-dimensional motion with constant speed must have zero acceleration

Acceleration is the rate of change of velocity with respect to time.
Velocity is speed plus a direction.

If the speed (magnitude of velocity) is constant then the only way there can be an acceleration is for the direction of the particle's motion to reverse.
If the reversal in direction happens with the particle maintaining constant speed the reversal in direction must happen instantaneously - the component of velocity against time graph is a step function.
Physically this is impossible as this would imply an infinite acceleration, $\displaystyle \lim_{\Delta t \to 0} \frac{\Delta v}{\Delta t}=\infty$, so the condition that the speed is constant also implies that the direction is constant.
This means that the velocity is constant so there can be no acceleration.

The statement is true.

Farcher
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