Question

A force applied by an engine of a train of mass $2.05\times {10}^6\text{kg}$ changes its velocity from $5\text{m/s}$ to $25\text{m/s}$ in $5\text{minutes}$. The power of the engine is

• A. $1.025\text{MW}$
• B. $2.05\text{MW}$
• C. $5\text{MW}$
• D. $6\text{MW}$

Answer 1

The correct option is B $2.05\text{MW}$

Power is defined as rate of change of energy
$\text{Power}=\frac{\text{Energy}}{\text{Time}}=\frac{\frac{1}{2}m(v^2-u^2)}{t}$
$P=\frac{1}{2}\times \frac{2.05\times {10}^6\times \left(\right(25{)}^2-\left(5{)}^2\right)}{5\times 60};$
$P=2.05\times {10}^6\text{W}=2.05\text{MW}$

Why this question ? "Average power is the average amount of energy converted per unit of time." "Here we are calculating average power, if it had been instantaneous we need to use $P=\overrightarrow{F}.\overrightarrow{V}$"