Usain Bolt is pretty fast. In the 2016 Olympics, Usain ran the 100-meter sprint

Question

Usain Bolt is pretty fast. In the 2016 Olympics, Usain ran the 100-meter sprint in 9.69 seconds to win the gold. However, he was just shy of the current world record holder's time of 9.58 seconds set in 2009. Let's see how fast this contender (we'll call him Runner B) really is... a) Find the average velocity of Usain Bolt and Runner B for the 100-meter sprint. Usain's uavg Runner B's uavg- b) Fitting the data from Runner B's world record holding race gives the accceleration versus time graph below. Create a velocity versus time plot for Runner B (assume that runner B starts from rest) a (m/s) Acceleration vs. Time 4 14 12 2 4 8 Time (seconds) Time (s) v (m/s)Time (s) v (m/s) 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Explanation / Answer

1)Vavg.=dispacement/time taken

Vussain avg.=100/9.69=10.319 ms-1

Runner B V avg.=100/9.58=10.438 ms-1

2)a = dV/dt

dV = a*dt

V = a dt..........(1)

here a as a function of t can be written as

7a=28-4t for 0<t<7 and a=0 for 7<t<8.......(2)

Substituting a value from (2) in (1) velocity at different vlues of time can be calculated

Time Velocity

0 0

1 3.71

2 6.85

3 9.42

4 11.42

5 12.85

6 13.71

7 14

8 14

From these data the graph can be made

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