2. 1D Motion / Kinematics

A cheetah spots a Thomson's gazelle, its preferred prey, and leaps into action, quickly accelerating to its top speed of 30 m/s, the highest of any land animal. However, a cheetah can maintain this extreme speed for only 15 s before having to let up. The cheetah is 170 m from the gazelle as it reaches top speed, and the gazelle sees the cheetah at just this instant. With negligible reaction time, the gazelle heads directly away from the cheetah, accelerating at 4.6 m/s² for 5.0 s, then running at constant speed. Does the gazelle escape? If so, by what distance is the gazelle in front when the cheetah gives up?

(III) Mary and Sally are in a foot race (Fig. 2–46). When Mary is 22 m from the finish line, she has a speed of 4.0 m/s and is 5.0 m behind Sally, who has a speed of 5.0 m/s. Sally thinks she has an easy win and so, during the remaining portion of the race, slows down at a constant rate of 0.40 m/s² to the finish line. What constant acceleration does Mary now need during the remaining portion of the race, if she wishes to cross the finish line side-by-side with Sally? <IMAGE>

A rubber ball is shot straight up from the ground with speed v₀. Simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest. At what height above the ground do the balls collide? Your answer will be an algebraic expression in terms of h, v₀, and g.

Suppose car A starts a race at time $t=0$ with a constant speed $v{a}_0$, and car B starts later at time $t=T$ with a higher constant speed $v{b}_0$ ($v{b}_0>v{a}_0$). How long after car B started the race will car B catch up with car A?

David is driving a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s² at the instant when David passes. What is her speed as she passes him?

Figure 2–55 shows the position vs. time graph for two bicycles, A and B. At which instant(s) are the bicycles passing each other? Which bicycle is passing the other?

You are 9.0 m from the door of your bus, behind the bus, when it pulls away with an acceleration of 1.0 m/s². You instantly start running toward the still-open door at 4.5 m/s. What is the maximum time you can wait before starting to run and still catch the bus?

(II) Two locomotives approach each other on parallel tracks. Each has a speed of 155 km/h with respect to the ground. If they are initially 9.5 km apart, how long will it be before they reach each other? (See Fig. 2–39.)

(III) Mary and Sally are in a foot race (Fig. 2–46). When Mary is 22 m from the finish line, she has a speed of 4.0 m/s and is 5.0 m behind Sally, who has a speed of 5.0 m/s. Sally thinks she has an easy win and so, during the remaining portion of the race, slows down at a constant rate of 0.40 m/s² to the finish line. What constant acceleration does Mary now need during the remaining portion of the race, if she wishes to cross the finish line side-by-side with Sally?

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A rubber ball is shot straight up from the ground with speed v₀. Simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest. What is the maximum value of h for which a collision occurs before the first ball falls back to the ground?

A police car at rest is passed by a speeder traveling at a constant 36 m/s. The police officer takes off in hot pursuit, accelerating at a constant 2.00 m/s². (a) How long does it take for the police officer to overtake the speeder? (b) Calculate the speed of the police car at the overtaking point.

A rubber ball is shot straight up from the ground with speed v₀. Simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest. For what value of h does the collision occur at the instant when the first ball is at its highest point?

A Porsche challenges a Honda to a 400 m race. Because the Porsche's acceleration of 3.5 m/s² is larger than the Honda's 3.0 m/s², the Honda gets a 1.0 s head start. Who wins? By how many seconds?

At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of $2.80$ m/s². At the same instant a truck, traveling with a constant speed of $20.0$ m/s, overtakes and passes the car. How fast is the car traveling when it overtakes the truck?

David is driving a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s² at the instant when David passes. How far does Tina drive before passing David?