Final answer:
The work done to accelerate a car with a mass of 1100 kg from 20 m/s to 31 m/s is calculated using the work-energy principle. By computing the change in kinetic energy, the work done is found to be 310550 joules.
Step-by-step explanation:
To determine how much work is done to accelerate a car with a mass of 1100 kg from a speed of 20 m/s to a speed of 31 m/s, you can use the work-energy principle. This principle states that the work done on an object is equal to the change in its kinetic energy. The kinetic energy (KE) of an object is given by the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity of the object.
The work done on the car is the change in kinetic energy:
Final kinetic energy: KE_final = 1/2 * 1100 kg * (31 m/s)^2
Initial kinetic energy: KE_initial = 1/2 * 1100 kg * (20 m/s)^2
Work done (W) = KE_final - KE_initial
Calculating this:
- KE_final = 1/2 * 1100 kg * 961 m^2/s^2 = 530550 J
- KE_initial = 1/2 * 1100 kg * 400 m^2/s^2 = 220000 J
- W = 530550 J - 220000 J = 310550 J
Therefore, the work done to accelerate the car is 310550 J.