2D kinematics question (2nd year of undergrad level.)

[caj1218]

Homework Statement

An automotive test track forms a curve in the horizontal xy plane specified by y(x) =γx^3 / 2 where γ = 0.2 m^-1/2 and x ≥ 0 . A car moves along the track, starting at rest at the origin at time t = 0 , and picking up speed in accordance with v = ct , where c = 4.8 m s^-2 . The coefficient of friction between the car and the track is μ = 0.5 . At what position x does the car start to skid?

Homework Equations

(c^2+(v^2/R)^2)^1/2>=μg looking for x where this is true; when μg<=equation x will be the position at which it starts slipping.

The Attempt at a Solution

I know that v(x)=ct; therefore ds/dt=ct; (1+(y'(x))^2)^1/2 dx=ctdt; Can integrate and solve for t; which I can then plug into the above equation and have it only in terms of x which is what I need.

 

[BvU]

Hello caj, welcome to the homework part of PF !

Is there a question here ? You look all set and ready to go, so why not work it out ?