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 ........... $u$.

The distance travelled by a particle is proportional to the square of time. Then,the particle travels with:

Consider a vehicle moving with a velocity $54 \,km/h$. At a distance of $400 \,m$ from the traffic light, brakes are applied. The acceleration of the vehicle after the application of brakes is $-0.3 \,m/s^2$. The vehicle's position relative to the traffic light is: (in $\,m$)

Give an example of a motion where $x > 0$,$v < 0$,and $a > 0$ at a particular instant.

The displacement and the increase in the velocity of a moving particle in the time interval of $t$ to $(t+1) s$ are $125 \ m$ and $50 \ m/s$,respectively. The distance travelled by the particle in $(t+2)^{th} s$ is . . . . . . $m$.

The position of a particle moving along the $x$-axis is given by $x = (-2t^3 + 3t^2 + 5) \ m$. The acceleration of the particle at the instant its velocity becomes zero is ....... $m/s^2$.