A body of mass m = 10^–2 kg is moving in a medium and experiences a frictional force F = –kv². Its initial speed is v₀ = 10 ms^–1. If, after 10 s, its energy is $${1 \over 8}mv_0^2$$, the value of k will be:

Velocity-time graph for a body of mass 10 kg is shown in figure. Work-done on the body in first two seconds of the motion is :

A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n² R t² where n is a constant. The power delivered to the particle by the force acting on it, is :

A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km and applies a constant frictional force $${W \over 20}$$ on the car. While moving uphill on the road at a speed of 10 ms⁻¹, the car needs power P. If it needs power $${p \over 2}$$ while moving downhill at speed v then value of $$\upsilon $$ is :