Use motion plots or equations to solve: a) A world record was set for the men\'s

Question

Use motion plots or equations to solve:

a) A world record was set for the men's 100-m dash in the 2008 Olympics Games in Beijing by Usain Bolt of Jamaica. Bolt came across the finish line with a time of 9.69s. If we assume that Bolt accelerated for 3s 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 19.30s. Using the same assumptions as for the 100-m dash, what was his maximum speed for this race?

Explanation / Answer

a)et his acceleration is a m/s^2.

then distance travelled in 3 seconds=0*3+0.5*a*3^2=4.5*a m

maximum speed reached=a*3 m/s

rest of the distance he covered in 9.69-3=6.69 seconds

then distance covered in 6.69 seconds=3*a*6.69=20.07*a

hence 4.5*a+20.07*a=100

solving for a , we get a=4.07 m/s^2

then his maximum speed=a*3=12.21 m/s

b)again let acceleration be a.

distance covered in 3 minutes=0.5*a*3^2=4.5*a

maximum speed=3*a

then total distance covered=200 m

==> 4.5*a+3*a*(19.3-3)=200

==>a=3.7453 m/s^2

then maximum speed=a*3=11.236 m/s

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