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A car engine generates a force of 10000 N to move the car 1.2 km in 2 minutes. What is the power of the engine?
1000 kW
100 kW
10 kW
200 kW
100 kW
Power is defined as the rate at which work is done or energy is transferred. By calculating the total work done (10000┬аN├Ч1200┬аm=1.2├Ч107┬аJ) and dividing it by the time taken (120┬аseconds), we get 100000┬аW or 100┬аkW.
Power is defined as the rate at which work is done or energy is transferred. By calculating the total work done (10000┬аN├Ч1200┬аm=1.2├Ч107┬аJ) and dividing it by the time taken (120┬аseconds), we get 100000┬аW or 100┬аkW.
Think of it like climbing a staircase; walking up slowly takes less power, while running up the same flight of stairs in half the time requires double the power output from your muscles.
W=FтЛЕd тАФ Work done is Force multiplied by displacement
P=tWтАЛ тАФ Power is Work done divided by time interval
The mechanical power is calculated using the relationship P=tWтАЛ, where work done W=F├Чd. In this scenario, the engine exerts a constant force to displace the vehicle over a distance, transforming chemical energy into mechanical kinetic energy. Since power is the time-derivative of work, the shorter the time taken to perform the same amount of work, the higher the required power output.
Work done by the engine is 10000┬аN├Ч1200┬аm=1.2├Ч107┬аJoules.
Time must be converted from minutes to seconds: 2┬аminutes=120┬аseconds.
The SI unit of power is the Watt (W), where 1┬аkW=1000┬аW.
Provides a quantitative measure of engine performance efficiency regarding time.
Assumes constant force, whereas real-world engine output varies with acceleration and air resistance.
Automotive engineering for vehicle performance rating.
Industrial machinery sizing and selection.
Conversion: 1.2┬аkm=1200┬аm.
Calculation: P=120┬аs1.2├Ч107┬аJтАЛ=105┬аW=100┬аkW.
Option A, C, and D are incorrect due to errors in unit conversion or arithmetic.
B is correct тАФ The power calculated using the formula P=tFтЛЕdтАЛ results in 100┬аkW.
Always ensure units are in SI standard (Newtons, Meters, Seconds) before performing calculations to avoid common decimal or magnitude errors.
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