Question

A graph of x versus t is shown in figure. Choose correct alternatives from below.

1. The particle was released from rest at t = 0.
2. At B, the acceleration a > 0.
3. At C, the velocity and the acceleration vanish.
4. Average velocity for the motion between A and D is positive.
5. The speed at D exceeds that at E.

Answer 1

a, c and e

Explanation:

We know that velocity v = dx/dt and the slope of x-t graph gives ‘us velocity. This implies slope = dx/dt for the graph.

As per the diagram, at point A the graph is parallel to time axis, hence dx

v = dx/dt = 0. As the starting point is A, hence we can say that the particle is starting from rest. Thus option (a) is correct.

At C, the graph changes slope, hence velocity also changes.

As the graph at C is almost parallel to the time axis, hence we can say that velocity vanishes. Hence option (c) is correct.

As the direction of acceleration changes, hence we can say that it may be zero in between.

From the graph, it is clear that | slope at D| > | slope at E |

Hence, the speed at D will be more than at E. Hence option (e) is correct.

Important point: Here, a negative slope does not mean less value. It represents the change in direction of velocity.