The accelerator of a train can produce a uniform acceleration of `0.25ms^(-2)` and its brake can produce a retardation of `0.5ms^(-2)` The shortest time in which the train can travel between two stations 8 km apart is x minutes and 10 s, if it stops at both stations. The value of x is.

Engine of a car can produce a maximum acceleration 2 m//s^(2) and its brakes can produce a maximum retardation 3 m//s^(2) . Minimum time in which the car can travel a distance 6 km is:

The engine of a motoecycle can produce a maximum acceleration of 5 m//s^(2) . Its brakes can produce a maximum retardation of 10 m//s^(2) . What is the minimum time in which the motorcycle can cover a distance of 1.5 km ?

A train starting from rest moves with a uniform acceleration of 0.2 m//s^(2) for 5 minutes . Calculate the speed acquired and the distance travelled in this time.

A body is moving along the +ve x-axis with uniform acceleration of -4ms^(-2) . Its velocity at x=0 is 10ms^(-1) . The time taken by the body to reach a point at x=12m is

A train is travelling at a speed of 90 km//h . Brakes are applied so as to produce a uniform acceleration of - 0.5 m//s^(2) . Find how far the train will go before it is brought to rest.

A particle is thrown upwards from ground it experiences a constant resistance force which can produce retardation of 2m/s^2 The ratio of time of ascent to the time to descent is (g=10m/s^ 2)

A train starts from station A with uniform acceleration a_(1) . For some distance and then groes with uniform retardation a_(2) for some more distance to come to rest at station B . The distance between stations A and B is 4 km and the train takes 1//5 h compete this journey. If accelerations are in km per mimute unit, then show that (1)/(a_(1)) +(1)/(a_(2)) =x . Find the value of x .

The brakes of a train which is travelling at 30 m//s are applied as the train passes point A. The brakes produce a constant retardation of magnitude 3lambda m//s^(2) until the speed of the train is reduced to 10 m//s . The train travels at this speed for a distance and is then uniformly accelerated at lambda m//s^(2) until it again reaches a speed of 30 m//s as it passes point B. the time taken by the train in travelling from A to B, a distance of 4 km, is 4 min. Sketch the speed time graph for this motion and calculate:- (i) The value of lambda (ii) Distance travelled at 10 m//s .