1

While solving some statement reasoning questions on my textbook, I came across this statement which says a particle in one dimensional motion moving with constant speed must have zero acceleration

I marked the statement as wrong as speed will remain constant even if the direction of velocity vector changes, which would imply nonzero acceleration. However the statement has been marked as right in the answer section. The reasoning says that if the particle rebounds instantly with the same speed, it implies infinite acceleration which is unphysical

I assume that acceleration has been implied as infinite as the direction of velocity during rebound changes within a very small amount of time. But that time interval tends to be zero,but is not actually zero. In that case, there is still some non zero acceleration acting. Even if we look at this from the angle of change in momentum, there is some kind of acceleration. So please tell me whether the given statement A body with constant speed must have zero acceleration is true or not.

Lune2009
  • 25

2 Answers2

4

tell me whether the given statement A body with constant speed must have zero acceleration is true or not

That statement is not true. However, that is not what the question asked. It asked

a particle in one dimensional motion moving with constant speed must have zero acceleration

Here this statement is true. It is specifically restricted to one-dimensional motion, which makes all the difference.

In one dimensional motion you cannot have acceleration perpendicular to the velocity, by definition. Since all acceleration is necessarily parallel to the velocity any acceleration will necessarily change the speed.

Can you please elaborate on the statement that acceleration component cannot be perpendicular to the velocity in 1d motion?

One dimensional motion is motion along a single straight line. For two lines to be perpendicular to each other you need at least a plane. A plane is a two-dimensional surface. On a single straight one dimensional line you can only have parallel and anti-parallel, you cannot have perpendicular.

Dale
  • 117,350
2

I think it's not a good problem statement, but I'd argue the statement "a particle in one dimensional motion moving with constant speed must have zero acceleration" is correct.

In the case of the particle bouncing off and changing direction, either this happens instantaneously, which is unphysical, as the textbook argues, or it happens over a short but finite time, which means the particle doesn't actually have constant speed.

David_h
  • 485