A car of mass 800kg attains a speed of 25m/s in 20 secs. The power developed in the engine is
-
1 . 25 x 104 W
- 2 . 50 x 104 W
- 1 . 25 x 106W
- 2 . 50 x 106 W
The correct answer is: A
Explanation
To calculate the power developed in the engine, we need to determine the work done and the time taken.
1. Calculate the final kinetic energy (KE) of the car:
\[
KE = \frac{1}{2}mv^2
\]
where \( m = 800 \text{ kg} \) and \( v = 25 \text{ m/s} \).
\[
KE = \frac{1}{2} \times 800 \, \text{kg} \times (25 \, \text{m/s})^2
\]
\[
KE = 0.5 \times 800 \times 625 = 250000 \text{ J} \, (\text{joules})
\]
2. Calculate the power (P) developed in the engine using the formula:
\[
P = \frac{W}{t}
\]
where \( W \) is the work done (in this case, equal to the kinetic energy calculated) and \( t \) is the time taken.
\[
P = \frac{250000 \, \text{J}}{20 \, \text{s}} = 12500 \text{ W} \, (\text{watts})
\]
Thus, the power developed in the engine is 12500 watts (or 12.5 kW).