Question

vProblem: A possible model for a sprinter's velocity is given by Vx=a(1-e^(-bt))where t is in seconds, vx is in m/s, and the constants a and b are characteristic of the sprinter. Assume Sprinter A runs the 100-meter dash following this prescription with a = 11.81 m/s and b = 0.6887 s-1. a) Find an expression for Sprinter A’s acceleration as a function of time t. b) Find an expression for the distance traveled by Sprinter A as w.r.t. time t. c) Plot Sprinter A’s position, velocity and acceleration as a function of time. d) What was Sprinter A’s acceleration at t = 0s? e) What was Sprinter A’s acceleration at t = 2.30s? f) How long does it take Sprinter A to complete the race? g) What is Sprinter A’s final velocity? RACETIME: Another sprinter (let’s call them Sprinter X) is set to challenge Sprinter A’s time in 100-meter dash. Sprinter X’s motion is modeled using a constant acceleration of 2.5 m/s2 for the entire race. h) How far from the start are the racers when the eventual winner takes the lead? i) Who completes the dash in the shortest time? By how much shorter? j) Plot the positon versus time curve for both racers together on single plot. k) Which is the more realistic model for a sprinter’s velocity and why?

Answer 1

The time taken by the sprinter to finish the race can be only found by hit and trial as we cannot solve distance equation for t. We will have to guess the value of t and solve for S(t) and see if the distance is coming around 100 m .

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Ven bt a, b values jiven 8-131 ms2 a)o= 8.134 e 8.134 e-1.5,401