Question

A 500-kg dragster accelerates from rest to a final speed of 110 m/s in 400 m (about a quarter of a mile) and encounters an average frictional force of 1200 N. What is its average power output in watts and horsepower if this takes 7.30 s?

a) 1.25 × 10^5 W, 167 hp
b) 1.50 × 10^5 W, 200 hp
c) 1.75 × 10^5 W, 234 hp
d) 2.00 × 10^5 W, 267 hp

Answer 1

The average power output of the dragster is approximately 65,753 watts and 88.3 horsepower.

Step-by-step explanation:

To calculate the average power output of the dragster, we can use the formula for power, which is given by:

Power = Work / Time

The work done by the dragster is equal to the force exerted on it multiplied by the distance it travels:

Work = Force x Distance

Since the dragster experiences a constant force and travels a known distance, we can plug in the values to find the work done. Then, we can divide the work by the given time to calculate the average power output of the dragster.

Using the given values:

Force = 1200 N

Distance = 400 m

Time = 7.30 s

Plugging in these values, we get:

Work = 1200 N x 400 m = 480,000 J

Power = 480,000 J / 7.30 s ≈ 65,753 W

To convert the power from watts to horsepower, we can use the conversion factor that 1 horsepower is equal to 746 watts:

Power (in hp) = Power (in W) / 746 = 65,753 W / 746 ≈ 88.3 hp

Therefore, the average power output of the dragster is approximately 65,753 watts and 88.3 horsepower.