Calculating Impact Force and Distance Traveled in Two Car Collision

[Pomar1]

Homework Statement

Two cars are in opposite to each other. First car is 1000kg, second car is 2000kg. First car moves towards the second one with a velocity of ( neglect friction between the car's wheels and the asphalt ):
a) 30 km/h
b) 40 km/h
c) 50 km/h
Second car stands still until the collision appears ( velocity = 0km/h ). Calculate the length of route traveled by the second car after the collision ( assume the friction coefficient between the car's wheelsand the asphalt as T = 0.5 ).
If needed simplify the calculations by assuming both cars can only move forward/backward and can not turn ( two points of mass in an inertial frame ).

Homework Equations

I think that pretty much only thing I need here is Newton's:
F = ma [ N = kg * m/s^2 ]
v = at -> a = v/t [ m/s * 1/s ]
Although there is other problem, described below.

The Attempt at a Solution

So I managed to calculate the force acting on the second car after an impact, simply by substituting them into:
F = ma [N] = m * v/t [ kg * m/s * 1/s ]
F30 = 1000 * 5.55 * 1/t^2
F40 = 1000 * 8.33 * 1/t^2
F50 = 1000 * 11.11 * 1/t^2

But how do I get the time for the equation? This bugs me, is there another equation for acceleration I can use there?

Also, when I calculate the forces, how do I actually calculate the path traveled by the car, when I have to include friction ( I believe without it, car would just go on and on, without stopping ).

 

[jackarms]

Try thinking about the problem in terms of momentum. The second is going to accelerate, yes, but at the end of the collision it will arrive at its final velocity, and this is really the only thing that you care about.

And for the path, it will be the car starting at some velocity and then decelerating to a stop on the road. You're right -- without friction it would just keep this velocity and keep going.