kinematics of particls question

[lpaine1331]

Here is another question maybe someone can help me out with.

"A car starts from rest and accelerates at a constant rate until it reaches 60 mi/hr in a distance of 230 ft. at which time the clutch is disengaged. The car then slows down to a velocity of 33mi/hr in an additional distance of 420 feet with a deceleration which is proportional to its velocity. find the time t for the car to travel the 650 feet.

any help would be great.
thanks

 

[kalyanram]

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.