During the first $18\,min$ of a $60\,min$ trip,a car has an average speed of $11\,m/s$. What should be the average speed for the remaining $42\,min$ so that the car has an average speed of $21\,m/s$ for the entire trip (in $,m/s$)?

$A$ car starts from rest and moves with a constant acceleration of $5 \,m/s^2$ for $10 \,s$ before the driver applies the brake. It then decelerates for $5 \,s$ before coming to rest. The average speed of the car over the entire journey is: (in $\,m/s$)

$A$ body is at rest at $x=0$. At $t=0$,it starts moving in the positive $x-$direction with a constant acceleration. At the same instant,another body passes through $x=0$ moving in the positive $x$ direction with a constant speed. The position of the first body is given by $x_{1}(t)$ after time $t$ and that of the second body by $x_{2}(t)$ after the same time interval. Which of the following graphs correctly describes $(x_{1}-x_{2})$ as a function of time $t$?

The figure shows the velocity $(v)$ of a particle plotted against time $(t)$.

$A$ particle moves along a straight line such that its retardation is proportional to its displacement. The loss in its kinetic energy for any displacement $x$ is proportional to:

The engine of a motorcycle can produce a maximum acceleration $5 \, m/s^2$. Its brakes can produce a maximum retardation $10 \, m/s^2$. What is the minimum time in which it can cover a distance of $1.5 \, km$?