A cheetah is hunting. Its prey runs for 3.06 s at a constant velocity of +8.90 m/s. Starting from rest, what constant acceleration must the cheetah maintain in order to run the same distance as its prey runs in the same time?

a soldier fires an anti-tank missile at a stationary tank 4850 meters distant. The missile is fired with an initial speed of 28.5 m/s and accelerates with a constant acceleration of 18.6 m/s^2 for 6.42 s. The missile then continues on with a constant speed until it hits its target.  What is the total time that it took the missile to hit the target from the moment it was launched?

A helicopter carrying Dr. Evil takes off with a constant upward acceleration of 7.0 m/s2m/s2. Secret agent Austin Powers jumps on just as the helicopter lifts off the ground. After the two men struggle for 11.0 ss, Powers shuts off the engine and steps out of the helicopter. Assume that the helicopter is in free fall after its engine is shut off, and ignore the effects of air resistance.   What is the maximum height above ground reached by the helicopter?   Powers deploys a jet pack strapped on his back 7.0 ss after leaving the helicopter, and then he has a constant downward acceleration with magnitude 3.0 m/s2m/s2. How far is Powers above the ground when the helicopter crashes into the ground?

A cart is given an initial velocity of 8.1 m/s and experiences a contestant acceleration of 3.4m/s2. What is the magnitude of the cart's displacement during the first 15s of its motion?

An object is initially at rest and subject to a constant acceleration of 1.59 m/s2. What amount of time will it take this object to undergo a displacement of 29 from its initial position?

A train, traveling at a constant speed of 22.0 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 1.40 m/s2.  The speed of the train after 6.40 s on the incline is 13.0 m/s How far has the train traveled up the incline after 6.40 s?

An object is subject to a constant acceleration of 4.16 m/s2 in the positive x direction. If it is initially at rest, what is its displacement in the x-direction at t = 8.99 s?

A rocket is fired straight up from rest with a net upward acceleration of 12 m/s2. After 10.0 s, the engine shuts off, but the rocket continues to coast upward with insignificant air resistance. What is the maximum the rocket reach from the ground?

A cart is given an initial velocity of 13.5 m/s and experiences a constant acceleration of 2.5 m/s2. What is the magnitude of the cart's displacement during the first 11 s of its motion?

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