A motorist driving a 1200-kg car on level ground accelerates from 20.0 m/s to 30.0 m/s in a time of 5.0s. Neglecting friction and air resistance, determine the average mechanical power in watts the engine must supply during this time interval.
Kinetic energy increase divided by time.
To determine the average mechanical power, we can use the formula:
Power = Work / Time
First, let's calculate the work done on the car. The work done is equal to the change in kinetic energy:
Work = (1/2) * mass * (final velocity^2 - initial velocity^2)
Given:
Mass (m) = 1200 kg
Initial velocity (v1) = 20.0 m/s
Final velocity (v2) = 30.0 m/s
Work = (1/2) * 1200 kg * ((30.0 m/s)^2 - (20.0 m/s)^2)
Calculating the work, we get:
Work = (1/2) * 1200 kg * (900 m^2/s^2 - 400 m^2/s^2)
= (1/2) * 1200 kg * 500 m^2/s^2
= 300,000 kg * m^2/s^2
Now, we need to substitute the value of work into the power formula:
Power = Work / Time
Given:
Time (t) = 5.0 s
Power = 300,000 kg * m^2/s^2 / 5.0 s
Power = 60,000 kg * m^2/s^3 or 60,000 watts
Therefore, the average mechanical power the engine must supply during this time interval is 60,000 watts.