Lions, like most predators, are capable of very rapid starts. From rest, a lion can sustain an acceleration of 9.5 m/s2 for up to one second. How much time does it take a lion to go from rest to a typical recreational runner’s top speed of 10 mph?

A cheetah at rest notices a gazelle standing at a distance of 150.0 m. At the same time the gazelle notices the cheetah. The gazelle accelerates at 2.0 m/s2 for 8.0 s, after which it has reached top speed. The cheetah accelerates at 2.5 m/s2 until it has reached its top speed of 115.2 km/h. It can only continue at this speed for 35 s. Will the cheetah catch the gazelle? If so, when and where?

Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s2 lasting for any length of time will not cause injury, whereas an acceleration greater than 1000 m/s2 lasting for at least 1 ms will cause injury. Suppose a small child rolls off a bed that is 0.36 m above the floor. If the floor is hardwood, the child's head is brought to rest in approximately 2.2 mm. If the floor is carpeted, this stopping distance is increased to about 1.2 cm. Calculate the magnitude and duration of the deceleration in both cases, to determine the risk of injury. Assume that the child remains horizontal during the fall to the floor. Note that a more complicated fall could result in a head velocity greater or less than the speed you calculate. Hardwood floor magnitude  m/s2 duration  ms Carpeted floor magnitude  m/s2 duration  ms

A teenager climbs a tree that is 40ft tall. Once at the top of the tree he drops a ball that takes 2 seconds to hit the ground. Determine its initial and final speeds.

A ball is thrown straight down with an initial speed of 3.2 m/s from a height of 5.0 m. What is the position of the ball after 2.6 s, in meters? Use g = 10 m/s2.

Chameleons catch insects with their tongues, which they can rapidly extend to great lengths. In a typical strike, the chameleon's tongue accelerates at a remarkable 240 m/s2 for 20 ms, then travels at constant speed for another 30 ms. During this total time of 50 ms, 1/20 of a second, how far does the tongue reach?

A train, traveling at a constant speed of 25 m/s, comes to an incline with a constant slope. While going up the incline, the train slows down with a constant acceleration of magnitude 1.8 m/s2. What is the speed of the train after 8.0 s on the incline?