A stone is falling from a mountain. The velocity of the stone is given by V = 9.8t. Draw its graph and find the velocity of the stone ‘4’ seconds after start.

If the position vector of the particle is given by vecr = 3 t^2 hati + 5t hatj + 4hatk . Find the velocity of the particle at t = 3s.

A stone of mass 2 kg is falling from a certain height. Find the force of attraction between the Earth and the stone. Also, find the acceleration.

A uniform rod of mass M and length a lies on a smooth horizontal plane. A particle of mass m moving at a speed v perpendicular to the length of the rod strikes it at a distance a/4 from the centre and stops after the collision. Find a. the velocity of the cente of the rod and b. the angular velocity of the rod abut its centre just after the collision.

The rectangualr wire- frame, shown in has a width d, mass m, resistance R and a large length. A uniform magnetic field B exists to the left of the frame. A constant force F starts pushing the frame into the magnetic field at t =0. (a) Find the acceleration of the frame when its speed has increased to v. (b) Show that after some time the frame will move with a constant velocity till the whole frame enters into the magnetic field. find this velocity v_0 . (c) show that the velocity at tiem t is given by v= v_0(1 - e^(-Ft/mv_0) .

A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a sin (wt + (pi)/6) . After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity ?

A stone is thrown up vertically. The height it reaches at time t seconds is given by x=80t-16t^(2) . The stone reaches the maximum height in time t seconds is given by

The velocity of a body is given by the equation v= b//t + ct^(2) + dt^(3) . Find the dimensional formula for b.

A stone is allowed to fall from a top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. The two stones will melt after :