$A$ particle of mass $m$ moving eastward with a speed $v$ collides with another particle of same mass moving northward with same speed $v$. The two particles coalesce after collision. The new particle of mass $2m$ will move in north-east direction with a speed (in $m/s$) of:

$A$ ball loses $15.0\%$ of its kinetic energy when it bounces back from a concrete wall. With what speed must you throw it vertically down from a height of $12.4\, m$ to have it bounce back to the same height (ignore air resistance)? ............. $m / s$

$A$ water pump is driven by a petrol engine that pumps water from a depth of $30 \ m$ at a rate of $0.5 \ m^3/min$. If the efficiency of the pump is $70\%$, what is the power generated by the engine in $W$?

$A$ body starts moving unidirectionally under the influence of a source of constant power. Which one of the graphs correctly shows the variation of displacement $(s)$ with time $(t)$?

$A$ truck of mass $M$ and a car of mass $\frac{M}{10}$ moving with the same momentum are brought to a halt by the application of the same braking force. The ratio of the distances travelled by the truck and the car before they come to a stop is

To simulate car accidents,auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass $1000 \; kg$ moving with a speed $18.0 \; km/h$ on a rough road having $\mu = 0.5$ and colliding with a horizontally mounted spring of spring constant $6.25 \times 10^{3} \; N m^{-1}$. What is the maximum compression of the spring in $m$?