I\'m having a little trouble with te algebra solving for the Normal forces of A

Question

I'm having a little trouble with te algebra solving for the Normal forces of A and B, any help will be appreciated.

The sports car has a mass of 1.5 Mg and a center of mass at G. Determine the shortest time it takes for it to reach a speed of 80 km/h, starting from rest, if the engine only drives the rear wheels, whereas the front wheels are free rolling. The coefficient of static friction between the wheels and the road is . Neglect the mass of the wheels for the calculation. If driving power could be supplied to all four wheels, what would be the shortest time for the car to reach a speed of 80 km/h? 0.2NA + 0.2NB = 1500aG (1) NA + NB - 1500(9.81) = 0 (2) -NA (1.25) + NB (0.75) - (0.2NA + 0.2NB)(0.35) = 0 (3)

Explanation / Answer

from equation 2 you have

Na+Nb=1500*9.81

form equation 3 you have

(-1.25-0.2*0.35)Na+(0.75-0.2*0.35)Nb=0

or

- 1.32 Na + 0.575 Nb=0

so Nb=1.32/0.575 Na

Nb= 2.29565 Na--------4

putting equation 4 in equation 2 we have

Na+2.2956Na=1500*9.8

or Na= 1500*9.8/(1+2.2956)

Na=4460.422 N

abd Nb= 1500*9.8-4460.42

Nb=10239.58 N

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