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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 . 33 × 10 2 s size 12{3 "." "33"´"10" rSup { size 8{-2} } " s"} {} , calculate the distance over which the puck accelerates.

0 . 799 m size 12{0 "." "799 m"} {}

A powerful motorcycle can accelerate from rest to 26.8 m/s (100 km/h) in only 3.90 s. (a) What is its average acceleration? (b) How far does it travel in that time?

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 . 0500 m/s 2 size 12{0 "." "0500 m/s" rSup { size 8{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 . 550 m/s 2 size 12{0 "." "550 m/s" rSup { size 8{2} } } {} , how long will it take to come to a stop from this velocity? (c) How far will it travel in each case?

(a) 28 . 0 m/s size 12{"28" "." "0 m/s"} {}

(b) 50 . 9 s size 12{"50" "." "9 s"} {}

(c) 7.68 km to accelerate and 713 m to decelerate

A fireworks shell is accelerated from rest to a velocity of 65.0 m/s over a distance of 0.250 m. (a) How long did the acceleration last? (b) Calculate the acceleration.

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 . 350 m/s 2 size 12{0 "." "350 m/s" rSup { size 8{2} } } {} , how far will it travel before becoming airborne? (b) How long does this take?

(a) 51 . 4 m size 12{51 "." 4" m"} {}

(b) 17 . 1 s size 12{"17" "." "1 s"} {}

Professional Application:

A woodpecker's brain is specially protected from large decelerations by tendon-like attachments inside the skull. While pecking on a tree, the woodpecker's head comes to a stop from an initial velocity of 0.600 m/s in a distance of only 2.00 mm. (a) Find the acceleration in m/s 2 and in multiples of g g = 9 . 80 m/s 2 size 12{g left (g=9 "." "80"" m/s" rSup { size 8{2} } right )} {} . (b) Calculate the stopping time. (c) The tendons cradling the brain stretch, making its stopping distance 4.50 mm (greater than the head and, hence, less deceleration of the brain). What is the brain's deceleration, expressed in multiples of g ?

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?

(a) 80 . 4 m/s 2 size 12{ - "80" "." 4" m/s" rSup { size 8{2} } } {}

(b) 9 . 33 × 10 2 s size 12{9 "." "33" times "10" rSup { size 8{ - 2} } " s"} {}

In World War II, there were several reported cases of airmen who jumped from their flaming airplanes with no parachute to escape certain death. Some fell about 20,000 feet (6000 m), and some of them survived, with few life-threatening injuries. For these lucky pilots, the tree branches and snow drifts on the ground allowed their deceleration to be relatively small. If we assume that a pilot's speed upon impact was 123 mph (54 m/s), then what was his deceleration? Assume that the trees and snow stopped him over a distance of 3.0 m.

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.

(a) 7 . 7 m/s size 12{7 "." "7 m/s"} {}

(b) 15 × 10 2 m/s 2 size 12{ - "15" times "10" rSup { size 8{2} } " m/s" rSup { size 8{2} } } {} . This is about 3 times the deceleration of the pilots, who were falling from thousands of meters high!

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Source:  OpenStax, Sample chapters: openstax college physics for ap® courses. OpenStax CNX. Oct 23, 2015 Download for free at http://legacy.cnx.org/content/col11896/1.9
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