$A$ small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of $10 \, m$ in $t \, s$,the distance travelled by the toy in the next $t \, s$ will be ......... $m$.

The displacement $(x)$ of a particle depends on time $t$ as $x = \alpha t^2 - \beta t^3$. Choose the incorrect statements from the following.

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 . . . . . . $m$.

Stopping distance of vehicles: When brakes are applied to a moving vehicle,the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity $(v_0)$ and the braking capacity,or deceleration,$-a$ that is caused by the braking. Derive an expression for stopping distance of a vehicle in terms of $v_0$ and $a$.

$A$ particle of mass $1\,kg$ is moving along the $x-$axis,where its velocity depends on the $x-$coordinate as $v = 2\sqrt{x}\,m/s$. Find the net force acting on the particle $2\,s$ after the start of motion.

Starting from rest,the acceleration of a particle is given by $a = 2(t - 1)$. The velocity of the particle at $t = 5 \, s$ is ......... $m/s$.