Question

A train is travelling at a speed of $90km{h}^{-1}$. Brakes are applied so as to produce a uniform acceleration of $-0.5m{s}^{-2}$. Find how far the train will go before it is brought to rest?

• A. $625m$
• B. $4050m$
• C. $8100m$
• D. $1250m$

Answer 1

The correct option is A $625m$

Given that,

Acceleration $a=-0.5m/s^2$

Speed $v=90km/h=25m/s$

Using equation of motion,

$v=u+at$

Where,

v = final velocity

u = initial velocity

a = acceleration

t = time

Put the value into the equation

Finally train will be rest so, final velocity,$v=0$

$0=25-0.5t$

$25=0.5t$

$t=\frac{25}{0.5}$

$t=50sec$

Again, using equation of motion,

$S=ut+\frac{1}{2}a{t}^2$

Where, s = distance

v = final velocity

u = initial velocity

a = acceleration

t = time

Put the value into the equation

Where S is distance travelled before stop

$s=25\times 50-\frac{1}{2}\times 0.5\times (50{)}^2$

$s=625m$

So, the train will go before it is brought to rest is $625m$.

Hence, A is correct.