Careful measurements have been made of olympic sprinters in the 100-meter dash. a quite realistic model is that the sprinter's velocity is given by vx =a(1-e^(-bt))
where t is in s, vx is in m/s, and the constants a and b are characteristic of the sprinter. sprinter carl lewis's run at the 1987 world championships is modeled with a= 11.81 m/s and b = 0.6887 s^-1.
a. what was lewis's acceleration at t= 0s?
b. what was lewis's acceleration at t = 2.10s ?
c. what was lewis's acceleration at t = 4.45s ?
d. find an expression for the distance traveled at time t .
e. your expression from part d is a transcendental equation, meaning that you can't solve it for t. however, it's not hard to use trial and error to find the time needed to travel a specific distance. to the nearest 0.01s , find the time lewis needed to sprint 100.0m . his official time was 0.01s more than your answer, showing that this model is very good, but not perfect.