Answer
(a) (i) The average acceleration is $5.59~m/s^2$
(ii) The average acceleration is $7.74~m/s^2$
(b) (i) The rocket travels 179 meters in the first 8.00 seconds.
(ii) The rocket travels 12.8 kilometers between 8.00 seconds and 1.00 minute.
Work Step by Step
$v_1 = (161~km/h)(\frac{1000~m}{1~km})(\frac{1~h}{3600~s}) = 44.7~m/s$
$v_2 = (1610~km/h)(\frac{1000~m}{1~km})(\frac{1~h}{3600~s}) = 447~m/s$
(a) average acceleration = $\frac{\Delta v}{\Delta t}$
(i) From t = 0 to t = 8.00 s:
$\frac{\Delta v}{\Delta t} = \frac{44.7~m/s- 0 }{8.00~s} = 5.59~m/s^2$
(ii) From t = 8.00 s to t = 1.00 min:
$\frac{\Delta v}{\Delta t} = \frac{447~m/s-44.7~m/s}{52.00~s} = 7.74~m/s^2$
(b)
(i) $y = \frac{1}{2}at^2$
$y = \frac{1}{2}(5.59~m/s^2)(8.00~s)^2$
$y = 179~m$
(ii) $y = v_0t+\frac{1}{2}at^2$
$y = (44.7~m/s)(52.00~s)+\frac{1}{2}(7.74~m/s^2)(52.00~s)^2$
$y = 12,800~m = 12.8~km$
