A top fuel drag racer with a mass of 500.0 kg completes a quarter-mile (402m) drag race in a time of 4.2s starting from rest. The car's final speed is 125m/s. What is the engine's average power output? Ignore friction and air resistance.
Divide the final kinetic energy by the time it takes to reach that velocity. That will be the average power and will have the dimensions of Watts.
You don't need to use the distance.
Acceleration was not constant during the interval, since the final velocity (125 m/s) was not twice the average (95.7 m/s)
To find the engine's average power output, we can use the formula:
Power = Work / Time
First, let's calculate the work done by the engine. The work done is equal to the change in kinetic energy, which can be calculated using the formula:
Work = (1/2) * mass * (final velocity^2 - initial velocity^2)
Here, the mass of the car is 500.0 kg, the final velocity is 125 m/s, and the initial velocity is 0 m/s (since the car starts from rest). Plugging in these values, we get:
Work = (1/2) * 500.0 kg * (125 m/s)^2
Next, we need to calculate the time it took for the car to complete the quarter-mile drag race. The time is given as 4.2 seconds.
Now, we can calculate the power:
Power = Work / Time
Substituting the values, we get:
Power = [(1/2) * 500.0 kg * (125 m/s)^2] / 4.2 s
Simplifying this expression gives us the average power output of the engine. Evaluating the expression will yield the final answer.