Thread: Kinematics: The Motion of Particles

A train takes 5 minutes to cover 3km between stations P and Q. Starting from rest at P, it accelerates at a constant rate to a speed of 40km/hr and maintains this speed for a while and then is brought uniformly to rest at Q. If the braking takes three times as long as the accelerate, find the time taken for the train to accelerate.

I worked out that 3000=0*t+0.5at^2+(100/9)*t+0.5a*3t^2+100/9*16t applies to the answer. and t=15s, a= (20/27)ms^-2

but how do you work t and a out?

Million thanks!

Hello BabyMilo

Originally Posted by BabyMilo

A train takes 5 minutes to cover 3km between stations P and Q. Starting from rest at P, it accelerates at a constant rate to a speed of 40km/hr and maintains this speed for a while and then is brought uniformly to rest at Q. If the braking takes three times as long as the accelerate, find the time taken for the train to accelerate.

I worked out that 3000=0*t+0.5at^2+(100/9)*t+0.5a*3t^2+100/9*16t applies to the answer. and t=15s, a= (20/27)ms^-2

but how do you work t and a out?

Million thanks!

Since the speed we're given is measured in km/hr, and the distance in km, let's suppose that the train accelerates for hr. So it brakes for hr and travels at constant speed for hr, since min hr.

Draw a velocity-time graph, which is in the form of a trapezium with horizontal, parallel sides of length (along the t-axis) and along the line where .

Now the area under this graph represents the distance travelled. So:

(sum of parallel sides) x (perpendicular distance between them)





hr.

So the acceleration time min seconds.

Grandad