Question

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, (a) calculate his maximum speed and (b) his acceleration

Answer 1

Vmax = 12.21m/s

`a = 4.07m/s^(2)`

Step-by-step explanation:

For the first 3 seconds:

`V_(3)=V_(o)+a*t=0+a*3=3a` This is the maximum speed. But we need acceleration.

`X_(3)=V_(o)*t+(a*t^(2))/(2) =(9*a)/(2)`

For the other 6.69s with constant speed:

`X_(t)=100=X_(3)+V_(3)*t`

`100=(9*a)/(2) +3*a*6.69` Solving for a:

`a = 4.07m/s^(2)` Now we replace this value on
`V_(3)=3a`:

`V_(3)=V_(max)=12.21m/s`