The $v-t$ plot of a moving object is shown in the figure. The average velocity of the object during the first $10$ seconds is...........$m/s$.

$A$ train starting from rest accelerates uniformly for $100\,s,$ then comes to a stop with a uniform retardation in the next $200\,s.$ During the motion,it covers a distance of $3\,km.$ Choose the wrong option.

Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $x_P(t) = at + bt^2$ and $x_Q(t) = ft - t^2$. At what time do the cars have the same velocity?

The graph below shows the velocity versus time graph for a body. Which of the following graphs represents the corresponding acceleration $v/s$ time graph?

$A$ scooter accelerates from rest for time $t_{1}$ at a constant rate $a_{1}$ and then retards at a constant rate $a_{2}$ for time $t_{2}$ and comes to rest. The correct value of $\frac{t_{1}}{t_{2}}$ will be ..... .

Consider a car initially at rest, starts to move along a straight road first with acceleration $5 \ m \ s^{-2}$, then with uniform velocity and finally, decelerating at $5 \ m \ s^{-2}$, before coming to a stop. Total time taken from start to end is $t = 25 \ s$. If the average velocity during that time is $72 \ km \ hr^{-1}$, the car moved with uniform velocity for a time of: (in $s$)