Kinematics and Dynamics

$v = u + at = 0 + 2.5(8) = 20\ \text{m s}^{-1}$ and $s = ut + \tfrac12 at^2 = \tfrac12(2.5)(64) = 80$ m.

$v = \dfrac{ds}{dt} = 6t^2 - 10t + 3$, so $v(2) = 24 - 20 + 3 = 7\ \text{m s}^{-1}$.

$v^2 = u^2 + 2as = 0 + 2(9.81)(45) = 882.9$, so $v = 29.7\ \text{m s}^{-1}$.

$s = \dfrac{(u+v)}{2}t = \dfrac{30+0}{2}(12) = 180$ m. The deceleration is $2.5\ \text{m s}^{-2}$.

$R - mg = ma$, so $R = m(g+a) = 70(11.31) = 791.7$ N — more than the weight of 686.7 N.

$4(6) + 0 = 4(3) + 2v$, so $24 = 12 + 2v$ and $v = 6\ \text{m s}^{-1}$.