The greatest speed limit in the United States is along the tolled section of Texas State Highway 130 where the limit is $85 \mathrm{mi} / \mathrm{h}$. How much time would be saved in driving that $41 \mathrm{mi}$ section at the speed limit instead of $60 \mathrm{mi} / \mathrm{h}$ ? (b) The speed limit in residential areas is commonly $25 \mathrm{mi} / \mathrm{h}$ but some motorists drive at an average speed of $45 \mathrm{mi} / \mathrm{h}$, perhaps by weaving through traffic and even driving through traffic lights that had just turned red. How much time would be saved in driving at that faster speed through $5.5 \mathrm{mi}$ instead of the posted speed limit if the car does not stop at any intersections?

When trailing a car on a highway, you are advised to maintain a trailing distance that is often quoted in terms of car lengths, such as in "stay back by 3 car lengths." Suppose the other car suddenly stops (it hits, say, a large stationary truck). Assume a car length $L$ is $4.50 \mathrm{~m}$, your car speed $v_0$ is $31.3 \mathrm{~m} / \mathrm{s}(70 \mathrm{mi} / \mathrm{h})$, your trailing distance is $n L=10.0 L$, and the acceleration magnitude at which your car can brake is $8.50 \mathrm{~m} / \mathrm{s}^2$. What is your speed just before colliding with the other car if (a) your reaction time $t_r$ to start braking is $0.750 \mathrm{~s}$ and (b) automatic braking is immediately started by your car's radar system that continuously monitors the road? What is the minimum value for $n$ needed to avoid a collision with (c) the reaction time $t_r$ and (d) automatic braking?

The silver ants of the Sahara Desert are the fastest ants in terms of their body length, which averages $7.92 \mathrm{~mm}$. In the hottest part of the day, they run as fast as $0.855 \mathrm{~m} / \mathrm{s}$. In terms of body lengths per second, how fast do they run?

A popular web video shows a jet airplane, a car, and a motorcycle racing from rest along a runway (Fig. 2.35). Initially the motorcycle takes the lead, but then the jet takes the lead, and finally the car blows past the motorcycle. Consider the motorcycle-car race. The motorcycle's constant acceleration $a_m=8.40 \mathrm{~m} / \mathrm{s}^2$ is greater than the car's constant acceleration $a_e=5.60 \mathrm{~m} / \mathrm{s}^2$, but the motorcycle has an upper limit of $v_m=58.8 \mathrm{~m} / \mathrm{s}$ to its speed while the car has an upper limit of $v_c=106 \mathrm{~m} / \mathrm{s}$. Let the car and motorcycle race in the positive direction of an $x$ axis, starting with their midpoints at $x=0$ at $t=0$. At what (a) time and (b) position are their midpoints again aligned?

The running event known as the $100 \mathrm{~m}$ dash consists of three stages. In the first, the runner accelerates to the maximum speed, which usually occurs at the $50 \mathrm{~m}$ to $70 \mathrm{~m}$ mark. That speed is then maintained until the last $10 \mathrm{~m}$, when the runner slows. Consider three parts of the record-setting run by Usain Bolt in the 2008 Olympics: (a) from $10 \mathrm{~m}$ to $20 \mathrm{~m}$, elapsed time of $1.02 \mathrm{~s}$, (b) from $50 \mathrm{~m}$ to $60 \mathrm{~m}$, elapsed time of $0.82 \mathrm{~s}$, and (c) from $90 \mathrm{~m}$ to $100 \mathrm{~m}$, elapsed time of $0.90 \mathrm{~s}$. What was the average velocity for each part?

Braking, no reaction time. Modern cars with a computer system using radar can eliminate the normal reaction time for a driver to recognize an upcoming danger and apply the brakes. For example, the system can detect the sudden stopping of a car in front of a driver by using radar signals that travel at the speed of light. Rapid processing then can almost immediately activate the braking. For a car traveling at $v=31.3 \mathrm{~m} / \mathrm{s}(70 \mathrm{mi} / \mathrm{h})$ and assuming a normal reaction time of $0.750 \mathrm{~s}$, find the reduction in a car's stopping distance with such a computer system.

A cream tangerine is thrown directly upward past three evenly spaced windows of equal heights. Rank the windows according to, (a) the average speed of the cream tangerine while passing them, (b) the time the cream tangerine takes to pass them, (c) the magnitude of the acceleration of the cream tangerine while passing them, and (d) the change Δν in the speed of the cream tangerine during the passage, greatest first.

The following equation gives the velocity $v(t)$ of a particle in four situations: $v=5 t^2-3$.

The following equation gives the velocity $v(t)$ of a particle in four situations: $v=3 t-4$/

The following equation gives the velocity $v(t)$ of a particle in four situations: $v=4 t^2+2 t-6$.

Figure 2-21 shows a general situation in which a stream of people attempt to escape through an exit door that turns out to be locked. The people move toward the door at speed $v_s=3.50 \mathrm{~m} / \mathrm{s}$, are each $d=0.25 \mathrm{~m}$ in depth, and are separated by $L=1.75 \mathrm{~m}$. The arrangement in Fig. $2-21$ occurs at time $t=0$. At what time does the layer's depth reach $5.0 \mathrm{~m}$ ? (The answers reveal how quickly such a situation becomes dangerous.)

The following equations give the velocity ν(t) of a particle in four situations: (a) ν = 3; (b) ν = 4t² + 2t - 6; (c) ν = 3t - 4; (d) ν = 5t² - 3. To which of these situations do the equations of Table 2-1 apply?

The following equations give the velocity $v(t)$ of a particle in four situations: $v=3 ;$ . To which of the situation do the equations of the mentioned table apply?

Figure $2.34$ is a plot of the age of ancient seafloor material, in millions of years, against the distance from a certain ocean ridge. Seafloor material extruded from that ridge moves away from it at approximately uniform speed. What is that speed in centimeters per year?