Question

A train starts from rest and moves with a constant acceleration of $2.0m{s}^{-2}$ for a half minute. The brakes are then applied and the train comes to rest in one minute. Find the total distance moved by the train.

• A. 1.7 km
• B. 2.7 km
• C. 3.7 km
• D. 4.7 km

Answer 1

The correct option is B 2.7 km

Distance traveled by train in 1 minute=$s_1=\frac{1}{2}a{t}^2=900m$

Velocity of train at the end of half minute=$v=u+at=2m/s^2\times 30s$

$=60m/s$

After half a minute, train comes to rest in one minute.

Hence $v=a_{brake}{t}_{brake}$

$a_{brake}=\frac{v}{t_{brake}}=1m/s^2$

Hence the distance traveled by train to come to rest is $s_2=\frac{v^2}{2a}$

$=\frac{{60}^2}{2\times 1}=1800m$
Hence total distance traveled=$s_1+s_2=2700m=2.7km$