A black automobile smashes into the rear of a white automobile stopped at a stop

Question

A black automobile smashes into the rear of a white automobile stopped at a stop sign. You investigate this collision and find that before the collision, the black automobile made skid marks 5.0 m long. After the collision, the black automobile made skid marks 1.0 m along (in the same direction as the initial direction of motion), and the white automobile made skid marks 2.00 m long. Both automobiles made these skid marks with all their wheels. The mass of the black automobile is 1120 kg, and the mass of the white automobile is 740 kg. The coefficient of sliding friction between the wheels and the pavement is 0.90.

(a) What is the speed of the black automobile just before the collision?
m/s

(b) What is the speed of the black automobile before it started to brake?
m/s

Explanation / Answer

speed of the automobile after the collision is v1

then accelaration a1 = fr/m =(mu_r*m1*g)/m1 = 0.9*9.81 = 8.83 m/s^2

then using v2^2 = v^2 -(2*a*S1)

0^2 = v1^2-(2*8.83*5)

v1 = 9.4 m/s

then just before the collison speed is u1 = v1*(m1+m2)/(m1_m2) = (9.4*(1120+740))/(1120-740) = 46 m/s

So the answers are

A) u1 = 46 m/s

B) v1 = 9.4 m/s

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