A cyclist moving on a level road at 4 m/s stops pedalling and lets the wheels come to rest. The retardation of the cycle has two components: a constant 0.08 `m//s^2` due to friction in the working parts and a resistance of `0. 02v^2//m`, where `v` is speed in meters per second. What distance is traversed by the cycle before it comes to rest? (consider ln 5=1.61).

A body is rolling on the ground with a velocity of 1 m/s. After travelling a distance of 5m, it comes to rest. Find the coefficient of friction.Take g = 10 m/s^2 .

An object moving with a speed of 6.25 "m.s"^(-1) is decelerated at a rate given by: (dv)/(dt) = -2.5 sqrt(v) where v is the instantaneous speed. What would be the time taken by the object to come to rest?

The force of resistance encountered by water on a motor boat of mass m going in still water with velocity v is proportional to the velocity vdot At t=0 when its velocity is v_0, then engine shuts off. Find an expression for the position of motor boat at time t and also the distance travelled by the boat before it comes to rest. Take the proportionality constant as k > 0.

A cyclist on a level road takes a sharp circular turn of radius 3 m (g = 10 ms^(-2) ). If the coefficient of static friction between the cycle tyres and the road is 0.2, at which of the following speeds will the cyclist not skid while taking the turn?

A body moving on the surface of the earth at 14 "m.s"^(-1) comes to rest due to friction after covering 50 m. Find the coefficient of friction between the body and the earth's surface. Given, acceleration due to gravity = 9.8 "m.s"^(-2) .