$A$ bogie of a uniformly moving train is suddenly detached from the train and stops after covering some distance. What is the relation between the distance covered by the bogie and the distance covered by the train in the same time?

Look at the graphs $(a)$ to $(d)$ carefully and state,with reasons,which of these cannot possibly represent one-dimensional motion of a particle.

The displacement $x$ of a particle depends on time $t$ as $x = \alpha t^2 - \beta t^3$.

The displacement of a particle moving in a straight line depends on time as $x = \alpha t^3 + \beta t^2 + \gamma t + \delta$. The ratio of initial acceleration to its initial velocity depends on:

$A$ person wearing a parachute jumps off a plane from a height of $2 \ km$ from the ground and falls freely for $20 \ m$ before his parachute opens. After his parachute opens, if he continues to move uniformly with the velocity attained due to his freefall, the total time taken by the person to reach the ground is (Acceleration due to gravity $= 10 \ m/s^2$) (in $s$)

Let $v$ and $a$ denote the velocity and acceleration respectively of a body. Which of the following statements is correct?