1. Convert Units
* Velocity: 15 km/h = 4.167 m/s (approximately) and 30 km/h = 8.333 m/s (approximately)
* Mass: 1000 kg (already in standard units)
2. Calculate the Change in Kinetic Energy
* Initial Kinetic Energy (KE₁): KE₁ = (1/2) * m * v₁² = (1/2) * 1000 kg * (4.167 m/s)² = 8680.56 J
* Final Kinetic Energy (KE₂): KE₂ = (1/2) * m * v₂² = (1/2) * 1000 kg * (8.333 m/s)² = 34722.22 J
* Change in Kinetic Energy (ΔKE): ΔKE = KE₂ - KE₁ = 34722.22 J - 8680.56 J = 26041.66 J
3. Work-Energy Theorem
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
* Work (W): W = ΔKE = 26041.66 J
Therefore, the work done to increase the car's velocity from 15 km/h to 30 km/h is approximately 26,041.66 Joules.
