2.5 Motion Equations for Constant Acceleration in One Dimension

A rocket accelerates at a rate of $\text{20 m}/\text{s}^{2}$ during launch. How long does it take the rocket to reach a velocity of 400 m/s?

A well-thrown ball is caught in a well-padded mitt. If the deceleration of the ball is $2 . \text{10} \times \text{10}^{4} \text{ m}/\text{s}^{2}$, and 1.85 ms $\left(\text{1 ms} = \text{10}^{- 3} \text{ s}\right)$ elapses from the time the ball first touches the mitt until it stops, what was the initial velocity of the ball?

(a) A light-rail commuter train accelerates at a rate of $1 . \text{35 m}/\text{s}^{2}$. How long does it take to reach its top speed of 80.0 km/h, starting from rest? (b) The same train ordinarily decelerates at a rate of $1 . \text{65 m}/\text{s}^{2}$. How long does it take to come to a stop from its top speed? (c) In emergencies the train can decelerate more rapidly, coming to rest from 80.0 km/h in 8.30 s. What is its emergency deceleration in $\text{m}/\text{s}^{2}$?

At the end of a race, a runner decelerates from a velocity of 9.00 m/s at a rate of $2 . \text{00 m}/\text{s}^{2}$. (a) How far does she travel in the next 5.00 s? (b) What is her final velocity? (c) Evaluate the result. Does it make sense?

In a slap shot, a hockey player accelerates the puck from a velocity of 8.00 m/s to 40.0 m/s in the same direction. If this shot takes $3 . \text{33} \times \text{10}^{- 2} \text{ s}$, calculate the distance over which the puck accelerates.

Freight trains can produce only relatively small accelerations and decelerations. (a) What is the final velocity of a freight train that accelerates at a rate of $0 . \text{0500 m}/\text{s}^{2}$ for 8.00 min, starting with an initial velocity of 4.00 m/s? (b) If the train can slow down at a rate of $0 . \text{550 m}/\text{s}^{2}$, how long will it take to come to a stop from this velocity? (c) How far will it travel in each case?

A swan on a lake gets airborne by flapping its wings and running on top of the water. (a) If the swan must reach a velocity of 6.00 m/s to take off and it accelerates from rest at an average rate of $0 . \text{350 m}/\text{s}^{2}$, how far will it travel before becoming airborne? (b) How long does this take?

An unwary football player collides with a padded goalpost while running at a velocity of 7.50 m/s and comes to a full stop after compressing the padding and his body 0.350 m. (a) What is his deceleration? (b) How long does the collision last?

Consider a grey squirrel falling out of a tree to the ground. (a) If we ignore air resistance in this case (only for the sake of this problem), determine a squirrel’s velocity just before hitting the ground, assuming it fell from a height of 3.0 m. (b) If the squirrel stops in a distance of 2.0 cm through bending its limbs, compare its deceleration with that of the airman in the previous problem.

Dragsters can actually reach a top speed of 145 m/s in only 4.45 s—considerably less time than given in the example and the example. (a) Calculate the average acceleration for such a dragster. (b) Find the final velocity of this dragster starting from rest and accelerating at the rate found in (a) for 402 m (a quarter mile) without using any information on time. (c) Why is the final velocity great…

In 1967, New Zealander Burt Munro set the world record for an Indian motorcycle, on the Bonneville Salt Flats in Utah, with a maximum speed of 183.58 mi/h. The one-way course was 5.00 mi long. Acceleration rates are often described by the time it takes to reach 60.0 mi/h from rest. If this time was 4.00 s, and Burt accelerated at this rate until he reached his maximum speed, how long did it take B…

(a) A world record was set for the men’s 100-m dash in the 2008 Olympic Games in Beijing by Usain Bolt of Jamaica. Bolt “coasted” across the finish line with a time of 9.69 s. If we assume that Bolt accelerated for 3.00 s to reach his maximum speed, and maintained that speed for the rest of the race, calculate his maximum speed and his acceleration. (b) During the same Olympics, Bolt also set the…