Irma is driving along a straight road leaving a parking lot at a shopping mall. The velocity, [math]v[/math][math]ms^{-1}[/math], of her car is given [math]v=\frac{1}{2}t^2-2t[/math] by the condition [math]t[/math] is the time in seconds after passing through the automatic barrier. The initial displacement of the car is 50 meters.[br][br]
(a) Determine the value of [math]t[/math], in seconds, when the car driven by Irma stops momentarily.
(b) Find the total distance, in [math]m[/math], traveled by the car in the first 7 seconds.
[math]\frac{113}{6}m[/math]
(c) Determine the velocity of the car in the first 6 seconds.