Question

In figure shows the position of a particle moving on the X-axis as a function of time.

Options

• The particle has come to rest 6 times.

• The maximum speed is at t = 6s.

• The velocity remains positive for t = 0 to t = 6s.

• The average velocity for the total period shown is negative. 

Answer 1

The particle has come to rest 6 times.

Explanation:
(a) The slope of the x–t graph gives the velocity. Here, 6 times the slope is zero. So, the particle has come to rest 6 times.

(b) As the slope is not maximum at t = 6 s, the maximum speed is not at t = 6 s.

(c) As the slope is not positive from t = 0 s to t = 6s, the velocity does not remain positive.

(d) Average velocity =\[\frac{\text{ Total displacement } }{\text{ Total time taken } } = \frac{x_{\text{ final } } - x_{\text{ initial } }}{t}\]

For the shown time (t = 6 s), the displacement of the particle is positive. Therefore, the average velocity is positive.