The coefficient of friction between a particle moving with some velocity `V_(0)` and the rough horizontal surface is `((V_(0))/(2 g t_(0)))`. Find how much kinetic energy is lost in time `t_(0)` due to friction :

A block of mass m moving with a velocity v_(0) on a rough horizontal surface from x=0 coefficient of friction is given by mu=mu_(0)=ax . Find the kinetic energy of the block as function of x before it comes to rest.

A block of mass m moving with a velocity v_(0) on a rough horizontal surface from x=0 coefficient of friction is given by mu=mu_(0)+ax . Find the kinetic energy of the block as function of x before it comes to rest.

A small block of mass m is plced over a long plank of mass M the coefficient of friction between then is mu ground is smooth At t = 0 m is given a velocity v_(1) and M a velocity v_(2) (gtv_(1)) as shown in figure After this M is maintained at constant celeration a(ltmu g) Initially there will be some relative motion between the block and the plank ,but after some time relative motion will cease and velocities of both will become Find the forward force acting on the plank before after t_(0) respectively.

A small block of mass m is plced over a long plank of mass M the coefficient of friction between then is mu ground is smooth At t = 0 m is given a velocity v_(1) and M a velocity v_(2) (gtv_(1)) as shown in figure After this M is maintained at constant celeration a(ltmu g) Initially there will be some relative motion between the block and the plank ,but after some time relative motion will cease and velocities of both will become Find the forward force acting on the plank before after t_(0) respectively.

If a charged particle is projected on a rough horizontal surface with speed v_(0) . Find the value of dynamic coefficient of friction, if the kinetic energy of system is constant.

If a charged particle is projected on a rough horizontal surface with speed v_(0) . Find the value of dynamic coefficient of friction, if the kinetic energy of system is constant.

A small body of mass m moving with velocity v_(0) on rough horizontal surface, finally stops due to friction. Find, the mean power developed by the friction force during the motion of the body, if the frictional coefficient mu =0.27,m=1 kg and v_(0)=1.5 ms^(-1) .

A particle moves with an initial velocity v_(0) and retardation alpha v , where v is the velocity at any time t.