A train of length 200 m is moving with uniform acceleration. It front and rear crosses a post beside the railtrack with velocities u and v respectively. Show that the mid-point of the train crosses the post with a velocity `sqrt((u^(2)+v^(2))/(2))`.

A particle is moving with a uniform acceleration along a straight line AB. Its velocity at A and B are 2 m/s and 14 m/s respectively. Then

The initial velocity is u and acceleration (f) is uniform. Final velocity and distance covered in the interval t are v and s respectively. Show that the velocity of the particle at half-distance is more than the velocity for half -time.

The initial velocity of a particle- is u and acceleration (f) is uniform. Final velocity and distance covered in the interval t are v and s respectively. Show that the velocity of the particle at half - distance is more than the velocity for half-time.

A body of mass m moving with a velocity u strikes elastically a stationary body of mass 2m . After the elastic collision the bodies move with velocities v and V respectively . Show that the body of mass m loses 8/9 part of its initial kinetic energy.

A body of mass in moving with a velocity u strikes elastically a stationary body of mass 2m. After 'the elastic collision 'the bodies move with velocities v and V respectively. Show that the body of mass m loses 8/9 part of its initial kinetic energy

A particle starting from a point A and moving with a positive constant acceleration along a straight line reaches another point B is time T. Suppose that the initial velocity of the particle is u gt0 and P is the midpoint of the line AB. If the velocity of the particle at point P is v_(1) and if the velocity at time (T)/(2) is v_(2) , then -

A train attains a velocity v after starting from rest with a uniform acceleration alpha . Then the train travels for sometime withuniform velocity, and at last comes to rest with a uniform retardation beta . If the overall displacement is s in time t , show that t = (s)/(v)+(v)/(2)((1)/alpha+(1)/(beta))

Two satellite of masses m_1 and m_2 (m_1 gt m_2) are revolving around the earth in orbits of radii r_1 and r_2 (r_1gt r_2) with velocities v_1 and v_2 respectively . In this case

A train moving with a constant acceleration crosses an observer standing on the platform. The first and the second compartments, each 15 m long cross the observer in 2s and 2.5 s, respectively. Find the velocity of the train when its first compartment just crosses the observer and also find its acceleration.