Question

Figure shows the position of a particle moving along the $x-$ axis as a function of time. Which of the following is correct?

• A. The particle has come to rest 6 times.
• B. The maximum speed is at $t=6\text{s}$.
• C. The velocity remains positive for $t=0$ to $t=6\text{s}$.
• D. The average velocity for the total period shown is negative.

Answer 1

1. The slope of the displacement time curve gives velocity
   There are six points in this graph where the tangents have zero slopes. So, the particle has come to rest 6 times during this entire motion.
2. At $t=6\text{s}$, the velocity will not be maximum as the slope at this point is parallel to $t$.
3. The velocity will not be positive all the time because the given curve has both positive and negative slopes from $t=0\text{sec}$ to $t=6\text{sec}$. So The average velocity will be positive from $t=0\text{sec}$ to $t=6\text{sec}$ as the total displacement is positive.

The correct option is D The particle has come to rest 6 times.