Question

a train starting from rest pick up a speed of 10 metre per second in 20 seconds. It continues to move at the same speed for the rest 50 seconds. It is then brought to rest in 20 seconds. Plot a speed time graph for the entire motion of the train

Answer 1

First let us plot the graph with the data given.

Let the starting point be the origin in the speed - time graph.




(a) Uniform rate of acceleration  = slope of AB
                                                = (20−0) (m/s)/ [(200−0) s]
                                                = 0.1 m/s2.

(b) Uniform retardation = − slope of CD

                                 = − (0−20)(m/s) /[(800−700)s]

                                 = 0.2 m/s2. 

(c) Total distance covered before stopping = area under the curve ABCD
                                                             = area of ΔABE + area of rectangle BCFE + area of ΔCDF
                                                             = ½ x 200 x 20 + 500 x 20 +  ½ x 100 x 20  m
                                                             = 2000 + 10000 + 1000   m
                                                             = 13,000 m = 13 km

(d) Average speed = Total distance covered/total time taken = 13000 m /(800 s)
                                                                                       = 16.25 m/s