30. ACCELERATION OF A CAR The distance s (in feet) covered by a car after t sec is given by $s = -t^3 + 8t^2 + 20t$ $(0 \le t \le 6)$
(a) Find a general expression for the car's velocity at any time t $(0 \le t \le 6)$.
(b) Find a general expression for the car's acceleration at any time t $(0 \le t \le 6)$.
(c) Determine the acceleration at times t = 0, 1, 2, $2 + \frac{2}{3}$, 3, 4, 5, and 6 seconds. Then explain what happens at $2 + \frac{2}{3}$ seconds.
(i) a(0) =
(ii) a(1) =
(iii) a(2) =
(iv) a($2\frac{2}{3}$) =
(v) a(3) =
(vi) a(4) =
(vii) a(5) =
(viii) a(6) =
WHAT HAPPENS AT TIME t = $2\frac{2}{3}$?
