Question

A force applied by the engine of a train of mass 2.05 x ${10}^{6}kg$ changes its velocity from 5 $m{s}^{-1}$ to 25 $m{s}^{-1}$ in 5 minutes. The power of the engine is then

• A. 1.025 MW
• B. 2.05 MW
• C. 5 MW
• D. 6 MW

Answer 1

The correct option is B 2.05 MW

Given that,

Mass of train, $m=2.05\times {10}^{6}Kg$

Time, $t=5minutes=300s$

$v=25m/s$

$u=5m/s$

Acceleration,

$a=\frac{v-u}{t}$

$a=\frac{25-5}{300}$

$a=\frac{2}{30}=\frac{1}{15}m/s^2$

Using equation of motion,

$v^2-u^2=2as$

${\left(25\right)}^2-{\left(5\right)}^2=2\times \frac{1}{15}\times s$

$s=4500m$

Power,

$P=\frac{workdone}{time}$

$P=\frac{F\times d}{t}$

$P=\frac{m\times a\times s}{t}$

$P=\frac{2.05\times {10}^6\times 1\times 4500}{15\times 300}$

$P=2.05\times {10}^{6}W$

$P=2.05MW$