Answer
(a) $a = \sqrt{\frac{P}{2mt}}$
(b) At t = 2 s:
v = 11 m/s
At t = 10 s:
v = 24.5 m/s
(c) At t = 2 s:
$a = 2.7~m/s^2$
At t = 10 s:
$a = 1.2~m/s^2$
Work Step by Step
(a) $v^2 = \frac{2P}{m}~t$
$v = \sqrt{\frac{2P}{m}~t}$
$a = \frac{dv}{dt}$
$a = \frac{1}{2}(\frac{2P}{m}~t)^{-1/2}~\frac{2P}{m}$
$a = \sqrt{\frac{P}{2mt}}$
(b) At t = 2 s:
$v = \sqrt{\frac{2P}{m}~t}$
$v = \sqrt{\frac{(2)(3.6\times 10^4~W)}{1200~kg}(2~s)}$
$v = 11~m/s$
At t = 10 s:
$v = \sqrt{\frac{2P}{m}~t}$
$v = \sqrt{\frac{(2)(3.6\times 10^4~W)}{1200~kg}(10~s)}$
$v = 24.5~m/s$
(c) At t = 2 s:
$a = \sqrt{\frac{P}{2mt}}$
$a = \sqrt{\frac{3.6\times 10^4~W}{(2)(1200~kg)(2~s)}}$
$a = 2.7~m/s^2$
At t = 10 s:
$a = \sqrt{\frac{P}{2mt}}$
$a = \sqrt{\frac{3.6\times 10^4~W}{(2)(1200~kg)(10~s)}}$
$a = 1.2~m/s^2$
