Question

In figure shows the position of a particle moving on the X-axis as a function of time.
(a) The particle has come to rest 6 times.
(b) The maximum speed is at t = 6s.
(c) The velocity remains positive for t = 0 to t = 6s.
(d) The average velocity for the total period shown is negative.
Figure

Answer 1

(a) 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 = $\frac{\mathrm{Total}\mathrm{displacement}}{\mathrm{Total}\mathrm{time}\mathrm{taken}}=\frac{x_{\mathrm{final}}-x_{\mathrm{initial}}}{t}$
For the shown time (t = 6 s), the displacement of the particle is positive. Therefore, the average velocity is positive.