1.Car acceleration and distance.
Sol: $a = \frac{v-u}{t} = \frac{36-0}{12} = 3 \text{ m/s}^2$. Distance $s = \frac{1}{2}a t^2 = \frac{1}{2}(3)(144) = 216 \text{ m}$.
2.Vertical throw $15 \text{ m/s}$ height and time.
Sol: $H = \frac{u^2}{2g} = \frac{225}{20} = 11.25 \text{ m}$. Total time $T = \frac{2u}{g} = \frac{30}{10} = 3 \text{ s}$.
3.Acceleration at $t=2\text{s}$ for $x = t^3 - 3t^2 + 2t$.
Sol: $v = 3t^2 - 6t + 2 \implies a = 6t - 6$. At $t=2$, $a = 6(2)-6 = 6 \text{ m/s}^2$.
4.Crossing time for two trains.
Sol: $v_1 = 10 \text{ m/s}$, $v_2 = 15 \text{ m/s}$. $v_{rel} = 25 \text{ m/s}$. Total distance = $200 \text{ m}$. Time $t = \frac{200}{25} = 8 \text{ s}$.
