The two ends of a train moving with constant acceleration pass a certain point with velocities $u$ and $3u$. The velocity with which the middle point of the train passes the same point is ........... $u$.

$A$ car moving with a velocity $6.25 \,ms^{-1}$ is decelerated with $2.5 \sqrt{v} \,ms^{-2}$ (where $v$ is the instantaneous velocity). The time taken by the car to come to rest is: (in $\,s$)

The $v^2$ versus $s$ graph of a particle moving in a straight line is shown in the figure. From the graph,some conclusions are drawn. State which statement is wrong?

$A$ particle located at $x = 0$ at time $t = 0$ starts moving along the positive $X$-direction with a velocity $v$ that varies as $v = \alpha \sqrt{x}$. The displacement of the particle with time is proportional to

$A$ particle moves according to the equation $y = a + bt + ct^2 - dt^4$. What are the initial velocity and initial acceleration of the particle?

$A$ car starts at time $t=0$ from an initial speed of $10 \,m/s$ and accelerates uniformly with $2 \,m/s^2$ on a straight road for time $0 \leq t \leq 10 \,s$. Let $S_1$ and $S_2$ be the distance covered by the car in time $3 \leq t \leq 4 \,s$ and $4 \leq t \leq 5 \,s$ respectively. The ratio $\frac{S_2}{S_1}$ is