The velocity V0 of a bullet, on passing through a plank of thickness 'd' is halved. suppose the retardation is proportional to the square of velocity , the time of penetration is

A body of mass m = 4 kg starts moving with velocity v_(0) in a straight line is such a way that on the body work is being done at the rate which is proportional to the square of velocity as given by P = beta v^(2) where beta = ( 0.693)/( 2) . Find the time elapsed in seconds before velocity of body is doubled.

If a point is moving in a line so that its velocity at time t is proportional to the square of the distance covered, then its acceleration at time t varies as

A motor boat of mass m moves along a lake with velocity V_(0) . At the moment t=0 the engine of the boat is shut down. Assuming the resistance of water is proportional to the velocity of the boat vecF=-rvecv Q. The velocity (v) of the motor boat as a function of the distance (s) covered with the shutdown engine is

A particle retards from a velocity v_(0) while moving in a straight line. If the magnitude of deceleration is directly proportional to the square loop of the speed of the particle, find its average velocity for the total time of its motion.

A solid metallic sphere of radius r is allowed to fall freely through air. If the frictional resistance due to air is proportional to the cross-sectional area and to the square of the velocity, then the terminal velocity of the sphere is proportional to which of the following ?

A bead moves along straight horizonal wire of length L , starting from the left end with a velocity v_(0) . Its retardation is proportional to the distance from the right end of the wire. Find the initial retardation (in m//s^(2) ) (at let end of the wire) if the bead reaches the right end of the wire with a velocity (v_(0))/2 . (given v_(0)=5m//s and L=1m )

A steamboat is moving at velocity v_0 when steam is shut off. It is given that the retardation at any subsequent time is equal to the magnitude of the velocity at that time. Find the velocity and distance travelled in time t after the steam is shut off.

The velocity of a bullet is reduced from 400 ms^(-1) to 100 ms^(-1) while travelling thought material of thickness of 1 m. The retardation will be

A particle is projected with velocity v_(0) along x - axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e. a=-x^(2) . The distance at which particle stops is -

Having gone through a plank of thickness h, a bullet changed its velocity from v_(0) to v_(1) . Find the time of motion of the bullet on the plank, assuming the resistance force to be proportional to the square of the velocity.