A race car starts from rest and travels east along a straight and level track. For the first $5.0s$ of the car's motion, the eastward component of the car's velocity is given by
$x\left(t\right)=\left(.960\frac{m}{s^3}\right)t^2$
What is the acceleration of the car when $v_x=15.5\frac{m}{s}$?
I tried to determine this by first assuming I need to find the velocity at $15.5\frac{m}{s}$, so I set the function above equal to that and solved it. I got a time and figured I needed to plug that into the second derivative of the function, but at $x''$ there is no $t$ to account for.
Any tips on what I did wrong would be greatly appreciated!
Set your velocity function equal to $15.5 \text{ m/s}$, and solve for $t$ to obtain the time time at which it will achieve this velocity.
Now, differentiate this function to obtain the acceleration $a(t)$ and find the acceleration at that time.