A car has an initial speed v0= 20m/s. It increases its speed along the circular track at s=0, at=(0.9s) m/(s2), where s is in meters. Determine the time needed for the car to travel 35m. The radius of curvature of the track is 40m.
an = v^2/p
a = dv/dt
The Attempt at a Solution
I really don't know how to approach the problem. I know that I want to define an integral that evaluates a change in s on one side with a change in t on the other.
I started by setting a = dv/dt = dv/ds * ds/dt = v * dv/ds so a * ds = v*dv. By doing this integral from 0 to 35m I found the final velocity to be 26.5 m/s. I do not know where to proceed from here.
Or can i solve that integral without inputting a value for s to get vf = sqrt ( 0.9s^2+400 ) ? Then using that I can do v = ds/dt so dt = (1/v) ds --> t = Integral [ 1/sqrt(0.9s^2+400) ds?