The position of the front bumper of a test car under microprocessor control is given by:
$x(t)=2.17m+\left(4.8\frac{m}{s^2}\right)t^2-\left(.100\frac{m}{s^6}\right)t^6$
Find its acceleration at the first instant when the car has zero velocity.
So I'm having trouble understanding where to start. I believe I need to take the derivative of the equation, but how do I find its acceleration when the car has zero velocity?
Any tips to get me started are greatly appreciated!
Best Answer
$$x(t)=2.17m+\left(4.8\frac{m}{s^2}\right)t^2-\left(.100\frac{m}{s^6}\right)t^6\\ v(t)=\left(9.6\right)t-\left(0.600\right)t^5$$ $v(t)=0$ when $t=0$ (first instant). So, $$a(0)=\left(9.6\frac{m}{s^2}\right)$$ This is indeed the magnitude of the gravitational acceleration.