Question

a train starts from station P with uniform acceleration a force of distance and there is goes to the uniform retardation 82 for some more distance to come to rest at the station to the distance between the station P and Q is 4 kilometre and the train takes 4 min to complete this journey it is acceleration are in kilometre /minute unit show that
1/a2+1/a2=2

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