A dragster drives a quarter mile (402 m) at a constant rate of acceleration, starting from rest and finishing the race with a final speed of 450 km/hr. The mass of the dragster, together with its driver, is 975 kg. What average power is provided by the engine, if 50% of the power output is delivered to the wheels? Neglect dissipative forces.

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Quizplus · Accepted Answer

The average power delivered to the wheels can be calculated using the work-energy principle and then accounting for the efficiency of power delivery. First, convert the final speed to meters per second: $450 \, \text{km/hr} = 450 \times \frac{1000}{3600} = 125 \, \text{m/s}$. The kinetic energy at the end of the quarter mile is $E_k = \frac{1}{2}mv^2 = \frac{1}{2} \times 975 \times (125)^2$. The work done is equal to this kinetic energy, and the power is work done per time. The time $t$ can be found from $v = at$ and $s = \frac{1}{2}at^2$, where $s = 402 \, \text{m}$, $v = 125 \, \text{m/s}$, and $a$ is the acceleration. Solving these equations gives $t$ and then $P = \frac{E_k}{t}$. Since only 50% of the engine's power output is delivered to the wheels, the total power output is twice the power calculated for the wheels. This calculation results in approximately 2.4 MW, considering the steps and the efficiency of power delivery.

A Dragster Drives a Quarter Mile (402 M) at a Constant