Answer:
To determine the work done by the engine of the car, we need to calculate the net work done on the car during the motion. The net work is given by the change in kinetic energy of the car:
net work = (1/2)mvf^2 - (1/2)mvi^2
where m is the mass of the car, vi is the initial velocity of the car, and vf is the final velocity of the car.
To calculate the final velocity of the car, we can use the equations of motion:
vf = vi + at
x = vi*t + (1/2)at^2
where x is the distance traveled by the car, a is the acceleration of the car, and t is the time taken to cover the distance x.
Using the given values of x = 250 m and t = 30 s, we can solve the second equation for a:
a = 2(x - vi*t) / t^2
where vi can be assumed to be zero since the car starts from rest. Substituting the given values, we get:
a = 2(250 m)/ (30 s)^2 = 0.3704 m/s^2
Now, we can use the coefficient of friction between the wheels and the ground to calculate the force of friction acting on the car:
f_friction = friction coefficient * normal force
where the normal force is the weight of the car, given by:
normal force = m * g
where m is the mass of the car and g is the acceleration due to gravity.
Substituting the given values of m = 1600 kg, g = 9.8 m/s^2, and the given coefficient of friction, we get:
f_friction = 0.03 * 1600 kg * 9.8 m/s^2 = 470.4 N
The force of friction acts in the opposite direction to the motion of the car, so we can find the net force acting on the car:
net force = f_engine - f_friction
where f_engine is the force generated by the engine of the car. We can assume that the force generated by the engine is constant, so we can use the equation:
f_engine = m * a
where m is the mass of the car and a is the acceleration of the car.
Substituting the given values of m = 1600 kg and the calculated value of a = 0.3704 m/s^2, we get:
f_engine = 1600 kg * 0.3704 m/s^2 = 592 N
Now we can find the net work done on the car by substituting the calculated values of f_engine and f_friction into the equation for net force:
net force = f_engine - f_friction = 592 N - 470.4 N = 121.6 N
The net work done on the car is then given by:
net work = net force * x
Substituting the given value of x = 250 m and the calculated value of net force, we get:
net work = 121.6 N * 250 m = 30,400 J
Therefore, the work done by the engine of the car is approximately 30,400 J.