Question

A point mass starts moving in a straight line with a constant acceleration a. At a time t₁ after the beginning of motion, the acceleration changes sign, remaining the same in magnitude.

Determine the time t from the beginning of motion in which the point mass returns to the initial position.

Answer 1

During a time t₁, the point mass moving with an acceleration a will cover a distance s = at₁²/2 and will have a velocity v = at₁. Let us choose the x-axis as shown in Fig. Here point O marks

the beginning of motion, and A is the point at which the body is at the moment t₁. Taking into account the sign reversal of the acceleration and applying the formula for the path length in uniformly varying motion, we determine the time t₂ in which the body will return from point A to point O:

The time elapsed from the beginning of motion to the moment of return to the initial position can be determined from the formula