Calculating the Work Required to Stop a Car

To calculate the work required to stop a car, we need to consider the kinetic energy of the car and the work done by the braking force to bring it to rest. The work done is equal to the change in kinetic energy of the car.

Given data:
Mass of the car (m) = 1500 kg
Initial velocity (v) = 60 km/h

Converting the velocity from km/h to m/s:
Since the SI unit of velocity is m/s, we need to convert the given velocity from km/h to m/s. We know that 1 km/h is equal to 0.2778 m/s.

Converting 60 km/h to m/s:
60 km/h * 0.2778 m/s = 16.67 m/s

Calculating the initial kinetic energy:
The initial kinetic energy (KE) of the car can be calculated using the formula:

KE = 0.5 * m * v^2

Substituting the values:
KE = 0.5 * 1500 kg * (16.67 m/s)^2
KE = 0.5 * 1500 kg * 277.78 m^2/s^2
KE = 231944.5 J

Calculating the final kinetic energy:
Since we want to bring the car to rest, its final velocity (vf) will be 0 m/s. Therefore, the final kinetic energy (KEf) will be 0.

KEf = 0 J

Calculating the work done:
The work done (W) is equal to the change in kinetic energy (ΔKE), which can be calculated as:

ΔKE = KEf - KE

Substituting the values:
ΔKE = 0 J - 231944.5 J
ΔKE = -231944.5 J

Since the work done is the negative of the change in kinetic energy, the work required to stop the car is also -231944.5 J. The negative sign indicates that work is done against the motion of the car.

Conclusion:
The work required to stop a car of 1500 kg moving at a velocity of 60 km/h is -231944.5 J. This negative work indicates that the braking force applied to stop the car is opposite to its motion, resulting in the reduction of its kinetic energy.