Question

A train starting from rest picks up a speed of 20 ms⁻¹ in 200 s. It continues to move at the same rate for the next 500 s and is then brought to rest in another 100 s.

1. Plot a speed-time graph.
2. From graph calculate
   (a) uniform rate of acceleration
   (b) uniform rate of retardation
   (c) total distance covered before stopping
   (d) average speed.

Answer 1

(i) 

(ii)
(a) Uniform rate of acceleration = Slope of v.t. graph from O to A.
= `"AE"/"OE"=20/200` = 0.1 ms⁻²

(b) Uniform rate of retardation = Slope of v.t. graph from BC
= `"BD"/"CD"=20/100` = 0.2 ms⁻²

(c) Total distance covered before stopping
= ar(ΔOAE) + ar(ΔABDE) + ar(ΔBCD)

= `1/2xx"OE"xx"AE"+"AE"xx"ED" + 1/2xx"BD"xx"DC"`

= `1/2xx200xx20+20xx500+1/2xx20xx100`

= 2000 + 10000 + 1000

= 13000 m 

= 13 km

(d) Average speed = `"Total distance covered"/"Total time taken"=13000/800`

= `130/8`

= 16.25 ms⁻¹