A driver in a 2000 kg Porsche wishes to pass a slow moving school bus on a 4 lane road. What is the average power in watts required to accelerate the sports car from 30 m/s to 60 m/s in 9 seconds?
Divide the K.E. change (in Joules) by 9 seconds.
(M/2)(V2^2 - V1^2)/9 = 300,000 W
That is about 400 Horsepower
To calculate the average power required to accelerate the sports car, we can use the formula for power:
Power = (Change in kinetic energy) / (Time)
First, let's calculate the change in kinetic energy:
Change in kinetic energy = (1/2) * mass * (final velocity^2 - initial velocity^2)
Given:
Mass (m) = 2000 kg
Initial velocity (u) = 30 m/s
Final velocity (v) = 60 m/s
Change in kinetic energy = (1/2) * 2000 kg * (60^2 m/s^2 - 30^2 m/s^2)
Let's simplify this equation:
Change in kinetic energy = (1/2) * 2000 kg * (3600 m^2/s^2 - 900 m^2/s^2)
Change in kinetic energy = (1/2) * 2000 kg * 2700 m^2/s^2
Change in kinetic energy = 1,350,000 kg⋅m^2/s^2
Now, let's calculate the average power:
Average power = (Change in kinetic energy) / (Time)
Given:
Time (t) = 9 seconds
Average power = 1,350,000 kg⋅m^2/s^2 / 9 seconds
Let's convert the unit of power from kg⋅m^2/s^2 to watts:
1 watt = 1 kg⋅m^2/s^2
Therefore,
Average power = 1,350,000 watts / 9 seconds
Finally, let's calculate the average power:
Average power = 150,000 watts
So, the average power required to accelerate the sports car from 30 m/s to 60 m/s in 9 seconds is 150,000 watts.
To calculate the average power required to accelerate the Porsche, we need to use the formula:
Power = (Work done) / (Time taken)
First, we need to calculate the work done. 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)
Given:
Mass of the Porsche (m) = 2000 kg
Initial velocity (v1) = 30 m/s
Final velocity (v2) = 60 m/s
Work = (1/2) * 2000 kg * ((60 m/s)^2 - (30 m/s)^2)
Now, let's simplify and calculate:
Work = (1/2) * 2000 kg * (3600 m^2/s^2 - 900 m^2/s^2)
= (1/2) * 2000 kg * 2700 m^2/s^2
= 2,700,000 kg*m^2/s^2
Next, we need to calculate the time taken, given as 9 seconds.
Now, we can use the formula for power and substitute the values:
Power = Work / Time
= 2,700,000 kg*m^2/s^2 / 9 s
Finally, let's calculate the average power:
Power = 300,000 kg*m^2/s^2 / 9 s
= 300,000 / 9 = 33,333.33 W (rounded to 2 decimal places)
Therefore, the average power required to accelerate the Porsche from 30 m/s to 60 m/s in 9 seconds is approximately 33,333.33 watts.