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Math  /  Algebra

Question5. The graph shows the kinetic energy of a car as the driver steps on the gas pedal. a) What is the power output of the car? b) If the process is 30\% efficient, determine the power delivered to the car.

Studdy Solution

STEP 1

1. The graph is linear, indicating a constant rate of change of kinetic energy over time.
2. The power output is the rate of change of kinetic energy with respect to time.
3. Efficiency is the ratio of useful power output to total power input.

STEP 2

1. Determine the power output of the car.
2. Calculate the power delivered to the car considering efficiency.

STEP 3

The power output is calculated as the slope of the kinetic energy vs. time graph.
The slope of the graph (power output) is given by the change in kinetic energy divided by the change in time.
Slope=ΔEkΔt=200 kJ−0 kJ60 s−0 s=200 kJ60 s \text{Slope} = \frac{\Delta E_k}{\Delta t} = \frac{200 \, \text{kJ} - 0 \, \text{kJ}}{60 \, \text{s} - 0 \, \text{s}} = \frac{200 \, \text{kJ}}{60 \, \text{s}}

STEP 4

Calculate the power output:
Power Output=200 kJ60 s=200,000 J60 s=200,00060 W \text{Power Output} = \frac{200 \, \text{kJ}}{60 \, \text{s}} = \frac{200,000 \, \text{J}}{60 \, \text{s}} = \frac{200,000}{60} \, \text{W}
Power Output=3333.3‾ W \text{Power Output} = 3333.\overline{3} \, \text{W}

STEP 5

Determine the power delivered to the car considering efficiency.
Given the efficiency is 30\%, the power delivered is the power output divided by the efficiency.
Power Delivered=Power OutputEfficiency=3333.3‾ W0.30 \text{Power Delivered} = \frac{\text{Power Output}}{\text{Efficiency}} = \frac{3333.\overline{3} \, \text{W}}{0.30}

STEP 6

Calculate the power delivered:
Power Delivered=3333.3‾0.30 W=11111.1‾ W \text{Power Delivered} = \frac{3333.\overline{3}}{0.30} \, \text{W} = 11111.\overline{1} \, \text{W}
The power output of the car is 3333.3‾ W 3333.\overline{3} \, \text{W} and the power delivered to the car is 11111.1‾ W 11111.\overline{1} \, \text{W} .

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