Answer to Question #169378 in Mechanical Engineering for Macdonald

Question

An electric train start from a station and maintained an acceleration of 0.9m/s² for 20 seconds, if it then travel for 80 seconds with uniform velocity and finally has a uniform retardation which brings it to rest in a further 10 seconds. calculate the retardation and the total distance covered.

Answer 1

Speed after 20 seconds:

$$v=at$$

Distance covered in 20 s:

$$d=vt/2$$

Distance covered in 80 seconds of uniform motion:

$$x=vT=atT$$

Retardation:

$$a_r=v/\tau=at/\tau=1.8\text{ m/s}^2.$$

Distance in retardation:

$$r=v\tau/2=at\tau/2$$

Total distance:

$$X=d+x+r=\\ =at(0.5+T+0.5\tau)=\\ =0.9·20(0.5+80+0.5·10)=1539\text{ m}.$$