The speeds of two identical cars are $u$ and $4u$ at a specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is

$A$ body lying initially at point $(3,7)$ starts moving with a constant acceleration of $4 \hat{i}$. Its position after $3 \,s$ is given by the coordinates ..........

Consider a particle moving along the positive direction of the $X$-axis. The velocity of the particle is given by $v = \alpha \sqrt{x}$ (where $\alpha$ is a positive constant). At time $t = 0$, the particle is located at $x = 0$. Find the time dependence of the velocity and the acceleration of the particle, respectively.

$A$ particle moves along a straight line in such a way that its acceleration is increasing at the rate of $2 m/s^3$. Its initial acceleration and velocity were $0$. The distance covered by it in $t = 3 s$ is ........ $m$.

Derive the equations of uniformly accelerated motion by the graphical method.

The velocity of a car travelling on a straight road is $3.6 \ km/h$ at an instant of time. Now, travelling with uniform acceleration for $10 \ s$, the velocity becomes exactly double. If the wheel radius of the car is $25 \ cm$, then which of the following is the closest to the number of revolutions that the wheel makes during this $10 \ s$?