Hi lipaine,
Having looked at your posts this problem could be a bit of a problem in the begining of Kinematics.
Here is how you solve it
Split the problem into two parts:
Part I
The particle is a uniform acceleration so you can solve this.
Part II:
Particle is a non-uniform acceleration here given deceleration is propotional to velocity.
let a be aceeleration v be velocity and s displacement. and c,b,k are constants
so a = -kv
v' = -kv
or v = ce^-kt, when you integrate this where c = 60mi/hr.
s' = 60e^-kt which gives s = (-60/k)e^-kt + b
we get b = 60/k at t =0;
so s= 60/k(1-e^kt) taking the condition s = 480 when v = 33 we have
k=9/160.
The rest of the result follows from here on.
I have felt three crucial assumptions which you have to figure out from what I have written above without which you will not be able to appreciate the problem.
Spend some time on this and you will be able to figure it out.
All the best for your homework.
~Kalyan.