Question

The velocity of a train is increased from $10m{s}^{-1}$to $25m{s}^{-1}$ in $2$ minutes due to the application of some force by its engine developing an average power of $525kW$. Neglecting frictional forces, the mass of the train must be

• A. 2.4 $\times {10}^4$ kg
• B. 2.4 $\times {10}^5$ kg
• C. 2.4 $\times {10}^6$ kg
• D. 2.4 $\times {10}^3$ kg

Answer 1

The correct option is B 2.4 $\times {10}^5$ kg

$\Delta K.E=\frac{1}{2}m(v^2-u^2)$
$W.D=\Delta K.E$
Power $=\frac{W.D}{t}=\frac{\frac{1}{2}m(v^2-u^2)}{2\times 60}$

$\Rightarrow 525\times {10}^3=\frac{1\times m({25}^2-{10}^2)}{4\times 60}$

$\Rightarrow m=2.4\times {10}^{5}kg$