Final answer:
To calculate the average force exerted by the truck's brakes, the work-energy theorem is used, resulting in a force of 16,666.67 newtons.
Step-by-step explanation:
Calculating the Average Force Exerted by the Brakes
To determine the average force exerted by the brakes on the truck that stops before hitting the deer, we can use the work-energy theorem. This principle states that the work done by the brakes is equal to the change in kinetic energy of the truck. Since the truck stops, the final kinetic energy is zero, and the initial kinetic energy can be calculated using the formula KE = 1/2 mv^2, where m is the mass of the truck and v is its initial velocity.
The work done by the brakes is also the product of the average force and the distance over which it is applied, i.e., Work = Force x distance. Since the truck stops, all the initial kinetic energy is dissipated by the work done by the brakes. By setting the work equal to the initial kinetic energy and rearranging the equation, we can solve for the force:
Force = (1/2 mv^2) / distance
In this case, with m = 500 kg, v = 50 m/s, and the stopping distance of 75 m, we can calculate the average force exerted by the brakes as follows:
Force = (1/2 * 500 kg * (50 m/s)^2) / 75 m = (1/2 * 500 * 2500) / 75 = 1250000 / 75 = 16666.67
The average force exerted by the brakes is therefore 16,666.67 newtons.