Question

Review 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 Ua(1-e- where t is in s, Ux 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 - 11.81m/s and b- 0.68875

Answer 1

a) V_x = a(1 - e^-bt) a_x = d_v_x/dt = (ae^-bt) times b At t = 0 sec a_x = 11.81 times 0.6887 times e^-0.6887 times 0 a_x = 8.134 m/s^2 b) At t = 2.2 sec a_x = 11.81 times 0.6887 times e^-0.6887 times 2.2 a_x = 1.788 m/s^2 c) At t = 4.05 sec a_x = 11.81 times 0.6887 times e^-0.6887 times 4.05 a_x = 0.4999 m/s^2 d) dx/dt = a [1 - e^-bt] d_x = a [1 - e^-bt] dt Integrating both sides x = integral a [1 - e^-bt] dt x = at - ae^-bt/-b x = at + a/b e^-bt