Compute the acceleration of the two cars after collision

Question

1. Car A was stopped when Car B hit Car A from behind
2. The two cars lock together and skid for 10 m before coming to a rest
3. The mass of Car A is 1800kg and the mass of Car B is 1200kg
4. The coefficient of kinetic friction between the tires and the road is 0.85

Answer 1

After the collision probably means that we are only interested in the motion after the cars have locked together. It's a little deceptive because it's worded like a conservation of momemtum problem. But it's really a free body diagram or Newton's second law problem.

After the collision, there is only one unbalanced force acting on the system: friction.

Newton's 2nd Law: ∑F=ma

Solving for a: a=∑F/m=f/m

(f = force of friction)

f=μF_N

F_N=mg

f=μmg

a=μmg/m=μg=0.85*9.8m/s^2=8.33m/s^2