Question

An engine developing an average power of $1500kW$ applies a steady force for $4minutes$ on a train moving with a velocity of $10m{s}^{-1}$. If there is no friction and the velocity attained by the train is $20m{s}^{-1}$, the mass of the train must be

• A. 240 tonnes
• B. 24 tonnes
• C. 2400 tonnes
• D. 2.4 tonnes

Answer 1

Answer: (C)

2400 tonnes

Power $=\frac{\Delta KE}{t}=\frac{\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2}{t}$
$\Rightarrow 1500\times {10}^3=\frac{\frac{1}{2}\times m\times (v^2-u^2)}{4\times 60}$
$\Rightarrow 1500\times {10}^3=\frac{\frac{1}{2}\times m\times ({20}^2-{10}^2)}{4\times 60}$

$\Rightarrow m=2400tonnes$