A racing car with mass (including the driver) of 900 kg accelerates from rest to a speed of 200 km/hr in 6 seconds. what is the power output of the engine?
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P= F•v=ma•v=m•(v/t) •v= m•v²/t =900•55.56²/6=4. 63•10^5 W
To determine the power output of the car's engine, we need to calculate the work done by the engine and divide it by the time it took to perform that work.
First, we need to calculate the work done by the engine. The work done is equal to the change in kinetic energy of the car.
The initial kinetic energy (K₁) is zero because the car starts from rest.
The final kinetic energy (K₂) can be calculated using the formula:
K₂ = (1/2) * m * v²,
where m is the mass of the car and v is the final speed.
Plugging in the given values:
m = 900 kg
v = 200 km/hr = (200 * 1000) / 3600 m/s = 55.56 m/s
K₂ = (1/2) * 900 kg * (55.56 m/s)²
Next, we calculate the change in kinetic energy (ΔK), which is equal to K₂ - K₁:
ΔK = (1/2) * 900 kg * (55.56 m/s)² - 0
Now we have the work done by the engine, which is equal to the change in kinetic energy:
Work = ΔK
Finally, we divide the work done by the time it took to perform that work to get the power output:
Power = Work / Time
The given time is 6 seconds.
Now, you can calculate the power output of the racing car's engine by substituting the values into the equation.