A train, initially at station A , starts its journey and eventually stops at station B after travelling a distance s . The first part of its journey is under uniform acceleration u and the later part under uniform retardation v . Show that the time taken for the journey is `sqrt(2s((1)/(u)+(1)/(v))).`

Two stations A and B are 2km apart. A train moves at first with a uniform acceleration a_(1) and then with a uniform retardation a_(2) to travel the distance AB in 4 min.Then

A train starts from a station and stops at another station. First the velocity of the train increases at a uniform rate, reaches a maximum velocity v and then starts decreasing at a constant rate. If the time spent for the entire journey is t, prove that the distance between the two stations is (1)/(2) vt.

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))

A train begins its journey from station A and stops at station B after 45 min. C is a certain point between A and B where the train attains its maximum velocity of 50 km. "h"^(-1) . If the train travels from A to C with a uniform acceleration and from C to B with a uniform retardation, calculate the distance between A and B.

A cyclist starts from place A and covers a distance of 2400 m to reach the place B. If the maximum possible acceleration of the cyclist is 2m//sec^2 and its maximum retardation is 4 m//sec^2 , what ts the least time the cyclist can undertake the journey from A to B ?

A body floats on a liquid with n-part of its volume immersed in the liquid. The body is released at a depth d inside the liquid. Show that it will reach the surface after a time sqrt((2(1-n)d)/(ng)) .

A train moves with uniform velocity u while going from station p to station Q. It returns along the same path with uniform velocity V. Its average velocity during the journey is :

During the n th second of its motion a body covers a distance s_(n) with uniform acceleration a and initial velocity u. Show that a = (2s_(n)-2u)/(2n-1) .