A train stopping at two stations 4 km apart takes 4 min on the journey from one of the station to the other. Assuming that it first accelerates with a uniform acceleration x and then that of uniform retardation y, prove that `1/x + 1/y = 2.`

A train goes from rest to rest between two stations with uniform acceleration and retardation. Find the rato of maximum velocity of the average velocity.

A particle starts moving from rest with uniform acceleration. It travels a distance x in the first 2 sec and a distance y in the next 2 sec. Then

A train starting from a railway station and moving with uniform acceleration attains a speed 40 km//h in 10 minutes. Find its acceleration.

Starting from rest a particle is first accelerated for time t_1 with constant acceleration a_1 and then stops in time t_2 with constant retardation a_2. Let v_1 be the average velocity in this case and s_1 the total displacement. In the second case it is accelerating for the same time t_1 with constant acceleration 2a_1 and come to rest with constant retardation a_2 in time t_3. If v_2 is the average velocity in this case and s_2 the total displacement, then

Starting from rest a particle is first accelerated for time t_1 with constant acceleration a_1 and then stops in time t_2 with constant retardation a_2. Let v_1 be the average velocity in this case and s_1 the total displacement. In the second case it is accelerating for the same time t_1 with constant acceleration 2a_1 and come to rest with constant retardation a_2 in time t_3. If v_2 is the average velocity in this case and s_2 the total displacement, then

The distance between two stations is 340 km. Two trains start simultaneously from these stations on parallel tracks to cross each other. The speed of one of them is greater than that of the other by 5 km/hr. If the distance between the two trains after 2 hours of their start is 30 km, find the speed of each train.

A train starts form station A at 1pm and reaches station B at 3pm, after travelling 108 km. It halts at station B for one hour and then starts for station C which is 42 km from station B . It reaches station C at 7pm on the same day. The average speed of the train for the whole journey from A to C is

A train moves from one station to another in two hours time. Its speed during the motion is shown in the graph Calculate (i) Maximum acceleration during the journey. (ii) Distance covered during the time interval from 0.75 hour to 1 hour

A car starts from erest accelerates uniform by for 4 second and then moves with uniform velocity which of the x-t graph represent th motion of the car:-

A body starts from rest and travels a distance x with uniform acceleration, then it travels a distance 2x with uniform speed, finally it travels a distance 3x with uniform retardation and comes to rest. If the complete motion of the particle is along a straight line, then the ratio of its average velocity to maximum velocity is