Final answer:
The amount of work done on the car is 6750 J.
Step-by-step explanation:
To calculate the work done on the car, we can use the work-energy theorem. The work done is equal to the change in kinetic energy of the car. Given that the gain in kinetic energy is 6750 J and the car speeds up to 3.0 m/s, we can use the formula:
Work = change in kinetic energy = 6750 J
Substituting the values into the formula: Work = (1/2) * mass * (final velocity^2 - initial velocity^2)
Work = (1/2) * 1500 kg * (3.0 m/s^2 - 0^2) = 6750 J
Therefore, the amount of work done on the car is 6750 J.