Calculate the force (in n) needed to bring a 1050 kg car to rest from a speed of 90.0 km/h in a distance of 125 m (a fairly typical distance for a non-panic stop).

F = 2625 N

Explanation:

let F be the force required to bring the car to stop, Ф be the angle between the force and the path of the motion,X be the distance it takes the car to come a complete stop, Kf be the final kinetic energy of the car and Ki be the kinetic energy of the car initially.

vi = 90.0/3.6 = 25 m/s

from Work and Energy, we know that:

Wtot = Kf - Ki

but Kf = 0J because the car's final velocity is 0 and W is the work done  by the force F

W = -Ki = -1/2(m×vi^2)

F×X×cos(Ф)  = -1/2(m×vi^2)

            -F×X = -1/2(m×vi^2)

                 F = (1/2)[(m×vi^2)/X]  

                 F = (1/2)[(1050×(25)^2)/125]  

                 F = 2625 N

therefore, the force need to put the car to a complete stop is 2625 N.