# Kinematics: One dimensional motion

If a particle is moving in one dimension with constant speed, can we say acceleration is zero at all the points? Answer given in my textbook is yes acceleration is zero.

But I think it can undergo a head on elastic collision and can have same speed in the opposite direction. But here it had acceleration during the instant of collision. So, as far as my knowledge goes, it can have non zero acceleration. Can someone throw some light, if I am thinking right?

Your textbook is almost, but not quite, telling you the truth. The problem is that word, "speed."

Acceleration is defined as the rate of change of velocity, not speed. Velocity is a vector quantity. Speed is a scalar (the magnitude of the velocity vector.) You can whirl a ball around your head on the end of a string at an approximately constant speed, but because the direction is continually changing, its velocity will never be constant, and its acceleration will never be zero.

Likewise, you could argue that the speed of a particle that instantaneously changes direction is, in some sense, "constant;" but because its direction changes, its velocity is not constant, and its acceleration is very far from zero during that "instant."

• But here we are taking about one dimensional motion. So change in direction is only possible when the particle reverses its direction. Even in that case speed will not be constant. It is first slow down, then zero and after that will increase in opposite direction. Solomon, what is your taken on this? – Arun Arora Oct 9 at 2:25
• @ArunArora, A one-dimensional vector space is somewhat of a degenerate case, but if the 1-D velocity of a particle changes from (-3) to 3, then I would say that the velocity is not constant, and therefore the acceleration is non-zero. – Solomon Slow Oct 9 at 13:41

An elastic collision will not have a constant speed.

To go in the opposite direction with the same speed, first it has to slow down as it hits the wall, then as it rebounds it will speed up in the other direction.

An object cannot instantly change velocity or reverse it's speed, that takes time; and during that time the speed would decrease and then increase again. What you are saying is true if an instantaneous collision and instantaneous change of direction were physically possible, but they are not.

• Thanks JMac, that is helpful – Arun Arora Oct 8 at 18:03