(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 . 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 world record in the 200 m dash with a time of 19.30 s Using the same assumptions as for the 100 m dash, what was his maximum speed for this race?
The relation between the distance d, time t, and the speed S is:
Here S is the speed of the body, and t is the time.
a) The bolt travels a portion of the total distance with a constant acceleration and the remainder at a maximal and constant speed.
The bolt travels a total distance 100 m . If a bolt travels d distance while accelerating, the remaining distance is 100-d , which is the distance he traveled at maximum speed.
Bolt accelerates for 3.00 s and then travels at a constant speed for the remaining 6.69 seconds.
Substitute 100-d for d’, S for average speed, and 6.69 s for t in the above equation:
The distance traveled by Bolt while accelerating can be calculated as:
Substituting the value of equation (2) in (1), we get:
The maximum speed of Bolt is .
The acceleration of the body can be calculated as:
Hence the acceleration of Bolt is
The entire distance traveled by Bolt is 200 m similar to the portion (a).
If Bolt travels d distance while accelerating, the remaining distance is 200-d which he traveled at maximum speed.
Bolt accelerates for 3.00 s , then travels at a constant speed for the following 16.30 s .
Substitute 100-d for d’’, S’’ for average speed and 16.30 sfor t in the above equation:
The distance traveled by Bolt while accelerating can be written as:
Substituting the value of equation (4) in (3), we get:
The maximum speed of Bolt is .
Dragsters can actually reach a top speed of in only considerably less time than given in Example 2.10 and Example 2.11.
(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 greater than that used to find the average acceleration?
Hint: Consider whether the assumption of constant acceleration is valid for a dragster. If not, discuss whether the acceleration would be greater at the beginning or end of the run and what effect that would have on the final velocity.
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 (6000m), 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 3.0m.
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