Question

A train starts from rest and accelerates uniformly at a rate of $2m{s}^{-2}$ for $10s$. It then maintains a constant speed for $200s$. The brakes are then applied and the train is uniformly retarded and comes to rest in $50s$. Find the total distance travelled.

• A. $4600km$
• B. $460m$
• C. $46m$
• D. $4600m$

Answer 1

The correct option is D $4600m$

The train completes its journey in three parts - uniform acceleration, uniform velocity and uniform retardation.

For uniform acceleration, $u=0,a=2m/s^2,t=10s$
$s_1=ut+\frac{1}{2}a{t}^2=0+\frac{1}{2}\times 2\times {10}^2=100m$
$v=u+at=0+2\times 10=20m/s$

Therefore, uniform velocity for the second part of journey = 20 m/s and time = 200 s
Distance $s_2=20\times 200=4000m$

For uniform retardation, $u=20m/s,v=0,t=50s$
From $v=u+at$
$0=20+50a$
$a=-0.4m/s^2$
$v^2=u^2+2as$
$s_3={20}^2/(2\times 0.4)=500m$

Total distance traveled, $s=s_1+s_2+s_3$
$s=100+4000+500=4600m$