An object starts sliding on a frictionless inclined plane,and from the same height,another object starts falling freely. Which of the following statements is correct?

$A$ particle of mass $m$ is moving along a circle of radius $R$ such that its tangential acceleration $a_t$ varies with distance covered $x$ as $a_t = \alpha x^2$, where $\alpha$ is a constant. The kinetic energy $K$ of the particle varies with the distance as $K = \beta x^c$, where $\beta$ and $c$ are constants. The values of $\beta$ and $c$ are:

The displacement-time graph of a particle moving in a straight line is as shown in the figure. Select the correct alternative.

Two bodies of unequal mass are moving in the same direction with equal kinetic energy. The two bodies are brought to rest by applying a retarding force of the same magnitude. How would the distance moved by them before coming to rest compare?

$A$ car moving with a velocity of $10 \, m/s$ can be stopped by the application of a constant force $F$ in a distance of $20 \, m$. If the velocity of the car is $30 \, m/s$,it can be stopped by this same force in what distance (in $, m$)?

$A$ body is released from a height of $30 \ m$ vertically downwards. The speed of the body at which potential energy is twice that of kinetic energy is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)