Final answer:
To increase the car's speed from 24.0 m/s to 35.0 m/s, we must calculate the change in kinetic energy using the car's mass and speeds, where the work done equals the change in kinetic energy.
Step-by-step explanation:
To calculate the work Wnet that must be done on the car to increase its speed from 24.0 m/s to 35.0 m/s, we can use the work-energy theorem. This theorem 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 equation KE = ½ mv2, where m is the mass of the object and v is its velocity.
Using the kinetic energy formula, the initial kinetic energy (KEi) when the car is moving at 24.0 m/s is:
KEi = ½ (1270 kg)(24.0 m/s)2
The final kinetic energy (KEf) when the car is moving at 35.0 m/s is:
KEf = ½ (1270 kg)(35.0 m/s)2
Now we subtract the initial kinetic energy from the final kinetic energy to find the change in kinetic energy (ΔKE), which is equal to the net work done (Wnet):
Wnet = KEf - KEi = ½ (1270 kg)(35.0 m/s)2 - ½ (1270 kg)(24.0 m/s)2
After crunching the numbers, we'll get the network required to increase the car's speed.