The plot shows the position (`x`) as a function of time (`t`) for two trains that run on a parallel track. Train `A` is next to train `B` at `t=0` and at `t=T_(0)`.

The graph shows position as a function of time for two trains running on parallel tracks. Which statement is true ?

Problems based on trains running on parallel track

A train of length L move with a constant speed V_(t) . A person at the back of the train fires a bullet at time t = 0 towards a target which is at a distance of D ( at time t = 0 ) from the front of the train ( on the same direction of motion ). Another person at the front of the train fires another bullet at time t = T towards the same target. Both bullets reach the target at the same time. Assuming the speed of the bullets V_(b) are same, the length of the train is

An experimenter is inside a uniformly accelerated train. Train is moving horizontally with constant acceleration a_(0) . He places a wooden plank AB in horizontal position with end A pointing towards the engine of the train. A block is released at end A of the plank and it reaches end B in time t_(1) . The same plank is placed at an inclination of 45^(@) to the horizontal. When the block is released at A it now climbs to B in time t_(2) . It was found that (t_(2))/(t_(1))= 2^((5)/(4)) . What is the coefficient of friction between the block and the plank?

A train accelerates from rest at a constant rate a for time t_(1) and then it retards at the constant rate b for time t_(2) then comes to rest. Find the ratio t_(1) / t_(2) .

A wave is propagating along the length of a string taken as positive x-axis. The wave equation is given by y=Ae^((-t/t-x/A)^(2)) where A=5mm, T=1.0 s and lambda=8.0 cm (a) Find the velocity of the wave. (b) find the function f(t) represent the displacement of particle at x=0. (c ) Plot the function g(x) representing the shape of the string at t=0 (d) Plot the function g(x) of the string at t=0 and t=5 s

Two stations A and B are 100km apart. A passenger train crosses station A travelling at a speed of 50 km//hr . The train maintains constant speed for 1 hour 48 minute and then the driven applies brakes to stop the train at station B in next 6 minute. Another express train starts from station B at the time the passenger train was crossing station A. The driver of the express train runs the train with uniform acceleration to attain a peak speed v_(0) . Immediately after the train attains the peak speed v_(0) , he applies breaks which cause the train to stop at station A at the same time the passenger train stops at B. Brakes in both the trains cause uniform retardation of same magnitude. Find the travel time of two trains and v_(0) .

Two trains A and B are running in the same directions on parallel tracks such that A is faster than B, packets of equal weight are exchanged between them. Then