Dynamics: Tangential and Normal Coordinates

[fabri010]

Homework Statement

A motorist starts from rest at point A on a circular entrance ramp when t=0, increases the speed of her automobile at a constant rate and enters the highway at point B. Knowing that her speed continues to increase at the same rate until it reaches 65 mi/h at point C, determine (a) the speed at point B, (b) the magnitude of the total acceleration when t=15s.
The entrance ramp is a quarter circle with radius 450 ft. Point B is at the point where the car stops moving in a circular path and begins to travel straight down the highway for 300 ft. when it reaches point C.

Homework Equations

s=s.+v.t+.5at^2

at=dv/dt et
an=((v^2)*t)/r

The Attempt at a Solution

vc=95.333 ft/s
s=225pi
stot=1006.8583
I have no idea how to complete this problem. If there was a time given to us I could figure out the at, and then use that to find the v and an. I feel like I'm not given enough information but I know that's wrong. If anyone could just put me in the right direction it would be greatly appreciated.

 

[Doc Al]

You have the distance (or should be able to figure it out). Using the average speed (which you should know), you can figure out the time.

Or you can look for another kinematic formula relating acceleration, speed, and distance.

 

[fabri010]

Yes I have that total time=21.12s, I calculated that. But I don't know how to find the time at B, when the car stops moving in a circular motion and begins to move linearly.

 

[Doc Al]

The translational acceleration doesn't change. Figure that out first.

 

[fabri010]

Thanks. I think I have it now.