A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to  where  and  are constants and  is the position of the particle. The acceleration of the particle as  function of , is given by:

If the velocity of a particle is , where  and  are constants, then the distance travelled by it between  and  is :

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time . On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time . The time taken by her to walk up on the moving escalator will be:

The speed of a swimmer in still water is . The speed of river water is  and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by:

A ball is thrown vertically downward with a velocity of 20  from the top of a tower. It hits the ground after some time with a velocity of . The height of the tower is :  ) 

The displacement-time graphs of two moving particles make angles of  and  with the -axis as shown in the figure. The ratio of their respective velocity is:       

The ratio of the distances travelled by a freely falling body in the 1st, 2nd, 3rd and 4th second:

A vehicle travels half the distance with speed  and the remaining distance with speed . Its average speed is

A bullet from a gun is fired on a rectangular wooden block with velocity . When bullet travels  through the block along its length horizontally, velocity of bullet becomes . Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is

A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity . The ball strikes the water surface after . The height of bridge above water surface is (Take  )