The 1800kg car B is stationary with its brakes locked when i

The 1800-kg car B is stationary with its brakes locked when it is rear-ended by the 2500-kg car A. After the impact, the cars become hooked together and slide 8 meters before coming to rest. The coefficient of kinetic friction between the road and the tires of car B is 0.8. At what speed was car A traveling immediately before the impact? Assume the brakes of car A were not applied.

use the figure in the question below

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Solution

((1800 + 2500) x g) x 0.8 = 33,712N.

braking force (g = 9.8 used).
Acceleration = (f/m) = 33,712/(2500 + 1800)

= -7.84m/sec^2.
Initial V of locked cars = sqrt.(2ad)

= sqrt.(15.68 x 8m)

= 11.2m/sec.
Initial momentum = (2500 + 1800) x 11.2

= 48,160kg/m/sec.
Car B was initially stationary, so had 0 momentum. Car A had it all.
Car A\'s V = (48,160/2500kg)

= 19.264m/sec. before the collision.