2002 ap physics c free response #1 question

[dlau]

hello, in lieu of the upcoming ap exam, I have been studying old free response questions from ap exams. I have a question about this one

A crash test car of mass 1000kg moving at constant speed of 12m/s collides completely inelastically with an object of mass M at time t=0. the object was initially at rest. the speed v in m/s of the car-object system after the collision is given as a function of time t in seconds by the expression

v=8/(1+5t)

(a)calculate the mass of the object
(b) assuming the initial position of x=0, determine an expression for the car object system after the collision as a function of time t
(c)determine an expression for the resisting force on the car-object system after the collision as a function of time t.
(d) determine the impulse delivered to the car-object system from t=0 to t=2s

I am currently doing A, and I came up with:

m1v1=(m1+m2)v2 <= (law of conservation)
(1,000)(12)=(1000+M)8

I got the 8 by plugging t=0 into v=8/(1+5t)

so M=1400KG? For some reason it does not seem right ...

[Doc Al]

so M=1400KG? For some reason it does not seem right ...
It's not. Your method is correct, but you must have made an arithmetic error.

[Doc Al]

hmm, alright, I got 500KG for the part a.
Right.

for part b, is it just integrating the v=8/(1+5t)?
Yep.

it looks like im stuck on part c ...
Think F = ma. You have v(t). Find a.

[dlau]

thanks! I solved it!