Assume the aerodynamic drag force on a car is proportional to its speed. If the power output from the engine is doubled, then the maximum speed of the car.

Answer carefully, with reasons :

$(a)$ In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact) ?

$(b)$ Is the total linear momentum conserved during the short time of an elastic collision of two balls ?

$(c)$ What are the answers to $(a)$ and $(b)$ for an inelastic collision ?

$(d)$ If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic ?

(Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).

Which one of the following statement does not hold good when two balls of masses ${m_1}$ and ${m_2}$ undergo elastic collision

When the momentum of a body increases by $100\%$, its $KE$ increases by .............. $\%$

A particle moves along $x$-axis from $x=0$ to $x=5$ metre under the influence of a force $F=7-2 x+3 x^2$. The work done in the process is .............

The kinetic energy acquired by a body of mass m is travelling some distance s, starting from rest under the actions of a constant force, is directly proportional to