A car accelerates from rest to a speed of 30 m/s. If the mass of the car is 800 kg, what is the work done on the car?

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Q: A car accelerates from rest to a speed of 30 m/s. If the mass of the car is 800 kg, what is the work done on the car?

Solution: Work done = Change in Kinetic Energy = 0.5 × mass × (final speed² - initial speed²) = 0.5 × 800 kg × (30 m/s)² = 360,000 J.

Steps: 9

Step 1: Identify the initial speed of the car. Since the car starts from rest, the initial speed is 0 m/s.
Step 2: Identify the final speed of the car. The final speed is given as 30 m/s.
Step 3: Identify the mass of the car. The mass is given as 800 kg.
Step 4: Use the formula for kinetic energy: Kinetic Energy = 0.5 × mass × speed².
Step 5: Calculate the change in kinetic energy. Since the initial speed is 0, the change in kinetic energy is equal to the final kinetic energy.
Step 6: Substitute the values into the formula: Kinetic Energy = 0.5 × 800 kg × (30 m/s)².
Step 7: Calculate (30 m/s)², which is 900 m²/s².
Step 8: Multiply 800 kg by 900 m²/s² to get 720,000 kg·m²/s².
Step 9: Multiply 720,000 by 0.5 to find the work done: 0.5 × 720,000 = 360,000 J.