The 1730-kg car has a velocity of 22 km/h up the 8-percent grade when the driver applies more power for 8 s to bring the car up to a speed of 50 km/h. Calculate the time average F of the total force tangent to the road exerted on the tires during the 8 s. Treat the car as a particle and neglect air resistance.

The time average F of the total force tangent to the road exerted on the tires during the 8s is 3091.04 N

Explanation:

Provided data from the problem

Velocity of the car V is 22km/h = 6.11m/s

Mass of the car m = 1730 kg

The time for which the driver apply the force t = 8s

The bringing speed of the car Vb = 50km/h = 13.89m/s

Equation to calculate the force by using the linear impulse momentum principle =

mV + Ft = mgsinαt + mVb ... eqn 1

Equation to calculate the sinα is

sinα = 1 / 1/√ (〖12〗^2 + 1^2)

sinα = 1/12.04

sinα = 0.083

substituting the value in equation 1, we have

(1730) (6.11) + F (8) = (1730) (9.81) (0.083) (8) + (1730) (13.89)

10570.3 + 8F = 11268.94 + 24029.7

8F = 35298.64 - 10570.3

8F = 24728.34

F = 24728.34 : 8

F = 3091.04 N