$A$ particle moves along the sides $AB, BC, CD$ of a square of side $25 \, m$ with a constant velocity of $15 \, m \, s^{-1}$. Its average velocity is ........ $m \, s^{-1}$.

Which of the following four statements is false?

Two buses $P$ and $Q$ start from a point at the same time and move in a straight line and their positions are represented by $X_{P}(t) = \alpha t + \beta t^{2}$ and $X_{Q}(t) = ft - t^{2}$. At what time,do both the buses have the same velocity?

Two stones are thrown up vertically and simultaneously but with different speeds. Which graph correctly represents the time variation of their relative position $\Delta x$? Assume that stones do not bounce after hitting the ground.

$A$ car is moving along a straight line,say $OP$ in the given figure. It moves from $O$ to $P$ in $18\; s$ and returns from $P$ to $Q$ in $6.0\; s$. What are the average velocity and average speed of the car in going from $O$ to $P$ and back to $Q?$

If a car covers $2/5^{th}$ of the total distance with speed $v_1$ and $3/5^{th}$ of the total distance with speed $v_2$,then the average speed is: