How much work must be done on a 500-kg car to accelerate it from 29-km/hr to 112-km/hr?

To calculate the work done, we need to use the formula:

Work = Change in Kinetic Energy.

The change in kinetic energy is equal to the final kinetic energy minus the initial kinetic energy.

First, we need to calculate the initial kinetic energy using the formula:

Kinetic Energy = 0.5 * mass * velocity^2.

Given:
Mass of the car (m) = 500 kg.
Initial velocity (v1) = 29 km/hr.

Converting km/hr to m/s:
1 km/hr = 1000 m/3600 s = 5/18 m/s.

So, initial velocity (v1) = 29 km/hr * (5/18) m/s = 145/18 m/s.

Now, we can calculate the initial kinetic energy:

Initial Kinetic Energy (KE1) = 0.5 * 500 kg * (145/18 m/s)^2.

Next, we calculate the final kinetic energy using the same formula but with the final velocity (v2):

Final velocity (v2) = 112 km/hr * (5/18) m/s = 280/9 m/s.

Final Kinetic Energy (KE2) = 0.5 * 500 kg * (280/9 m/s)^2.

Now, we can find the change in kinetic energy:

Change in Kinetic Energy = KE2 - KE1.

Finally, the work done on the car is equal to the change in kinetic energy.

Therefore, the amount of work that must be done on the car to accelerate it from 29 km/hr to 112 km/hr can be calculated using the given values and formulas.