A boy is pushing a box on a horizontal floor from a position of rest to rest, while moving along a straight line. Consider the three phases of motion. The floor is rough with a small friction coefficient. (i) Initially a constant hard push on the box to get it moving and attain a maximum velocity. (ii) Mild push to keep the box moving with constant velocity. (iii) To pull back the box to bring it to stop with the same retardation. Which of the following graphs is CORRECT?

Question

A boy is pushing a box on a horizontal floor from a position of rest to rest, while moving along a straight line. Consider the three phases of motion. The floor is rough with a small friction coefficient. (i) Initially a constant hard push on the box to get it moving and attain a maximum velocity. (ii) Mild push to keep the box moving with constant velocity. (iii) To pull back the box to bring it to stop with the same retardation. Which of the following graphs is CORRECT? (A) Option 1

(B)

(C)

(D)

Tardigrade Admin · Accepted Answer

The velocity of the box is always only in one direction. It is just increased and decreased during the motion, without changing its direction. Hence, velocity cannot be negative.
For the same reason, the direction of the friction also does not change and the friction is constant and always acts at the limiting value.
Acceleration is zero in the middle part of the motion as it is given that the velocity becomes constant. Hence, in the acceleration-time graph, the middle portion should be zero.
The worker first pushed the block harder to get it started, then he exerts some less force to sustain the motion and lastly, he reverses the direction of force to make the box retard. Also, he only exerts forces of constant magnitudes.