A car moving at a constant velocity of $46 \mathrm{m} {\mathrm{s}}^{-1}$ passes a traffic cop who is readily sitting on his motorcycle. After a reaction time of $1.0 \mathrm{s},$ the cop begins to chase the speeding car with a constant acceleration of $4.0 \mathrm{m} {\mathrm{s}}^{-2}$ . How much time does the cop need to overtake the speeding car?

You are driving towards a traffic signal when it turns yellow. Your speed is the legal speed limit of $v_0=55 \mathrm{km} {\mathrm{h}}^{-1}$. Your best deceleration rate has the magnitude, $a=5.18 \mathrm{m} {\mathrm{s}}^{-2}$. Your best reaction time to begin braking is $T=0.75 \mathrm{s}$. To avoid having the front of your car enter the intersection after the light turns red, should you brake to stop or continue to move at $55 \mathrm{km} {\mathrm{h}}^{-1}$ if the distance to the intersection and the duration of the yellow light are:
(a) $40 \mathrm{m}$ and $2.8 \mathrm{s}$ and
(b) $32 \mathrm{m}$ and $1.8 \mathrm{s}$?
Give an answer of the brake, continue, either (if either strategy works), or neither (if neither strategy works and the yellow duration is inappropriate).

You are arguing over a cell phone while trailing an unmarked police car by $25 \mathrm{m}$. Both your car and the police car are travelling at $120 \mathrm{km} {\mathrm{h}}^{-1}$. Your argument diverts your attention from the police car for $2.0 \mathrm{s}$ (long enough for you to look at the phone and yell, "I won't do that!"). At the beginning of that $2.0 \mathrm{s}$, the police officer begins braking suddenly at $5.0 \mathrm{m} {\mathrm{s}}^{-2}$.
(a) What is the separation between the two cars when your attention finally returns? Suppose that you take another $0.40 \mathrm{s}$ to realise your danger and begin braking.
(b) If you also brake at $5.0 \mathrm{m} {\mathrm{s}}^{-2}$, what is your speed when you hit the police car?

When a high-speed passenger train travelling at $161 \mathrm{km} {\mathrm{h}}^{-1}$ rounds a bend, the engineer is shocked to see that a locomotive has improperly entered onto the track from a siding and is a distance $D=676 \mathrm{m}$ ahead. When the locomotive is moving at $29.0 \mathrm{km} {\mathrm{h}}^{-1}$, the engineer of the high-speed train immediately applies the brakes. (a) What must be the magnitude of the resulting constant deceleration if a collision is to be just avoided? (b) Assume that the engineer is at $x=0$ when at $t=0$, he first spots the locomotive. Sketch $x\left(t\right)$ curve for the locomotive and high-speed train for the cases in which a collision is just avoided and is not quite avoided.

A man releases a stone at the top edge of a tower. During the last second of its travel, the stone falls through a distance of $\left(\frac{9}{25}\right) \text{h},$ where $\text{h}$ is the tower's height. Find $\text{h}$.