An example to illustrate the concepts used in the Velocity-Time graph

1996 Leaving Certificate Ordinary Level

A train,starting from rest, is uniformly accelerated to reach a speed of v m/s in 100s over 500m.
The speed of v m/s is maintained for a further 1500 m and the train is then brought to rest in the next 250 m under uniform retardation.
(i) Find the value of v
(ii) Find the acceleration and retardation
(iii) Find the total time
(iv) Draw an accurate velocity-time graph.

Area of left triangle =
 

Acceleration = 

Area of rectangle = 10X = 1500      X = 150s

Area of right triangle = 

Total Time = 100 150 50 = 300 s

Retardation =