A quite realistic model is that the sprinter’s velocity is given by -
vx = a (1 - e-bt) { eq.1 }
where, t = time measured in (s)
vx = velocity of sprinter’s measured in (m/s)
a & b = charateristic of the sprinter
Differentiating an above eq. w.r.t time & we get
(dvx / dt) = d [a (1 - e-bt)] / dt
ax = a b e-bt { eq.2 }
Part B : What was Lewis's acceleration at t = 2.06 sec?
Using eq.2 ; ax = a b e-bt
ax = (11.81 m/s) (0.6887 s-1) e-[(0.6887) (2.06)]
ax = [(8.134 m/s2) (0.2420)]
ax = 1.968 m/s2
Part C : What was Lewis's acceleration at t = 4.25 sec?
Using eq.2 ; ax = a b e-bt
ax = (11.81 m/s) (0.6887 s-1) e-[(0.6887) (4.25)]
ax = [(8.134 m/s2) (0.0535)]
ax = 0.4351 m/s2
Part D : Find an expression for the distance traveled at time (t).
We know that, x = vx t
Integrating an above eq. with a proper limit, we have
x (t) = vx
dt =
[a
(1 - e-bt)] dt
x (t) = a dt
+ a
e-bt
dt
x (t) = a t + (a / b) (e-bt - 1)
Part E : To the nearest 0.01 sec, find the time Lewis needed to sprint 100 m.
Assume at t = 10 s, we have
x (10) = [(11.81 m/s) (10 s)] + [(11.81 m/s) / (0.6887 s-1)] {e-[(0.6887) (10)] - 1}
x (10) = 100.97 m
Assume at t = 9.95 s, we have
x (9.95) = [(11.81 m/s) (9.95 s)] + [(11.81 m/s) / (0.6887 s-1)] {e-[(0.6887) (9.95)] - 1}
x (9.95) = 100.38 m
Assume at t = 9.92 s, we have
x (9.92) = [(11.81 m/s) (9.92 s)] + [(11.81 m/s) / (0.6887 s-1)] {e-[(0.6887) (9.92)] - 1}
x (9.92) = 100.025 m
Problem 2.82 What was Lews's aoceleration at 206 Careful meaturements have been made ef Olymple pier...
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 Part A What was Lewis's acceleration at t0s? Express your answer using four significant figures Submit...
l Review What was Lewis's acceleration at t 4.20 s Careful measurements have been made of Olympic sprinters in the 100- Express your answer using four significant figures meter dash. A quite realistic model is that the sprinter's velocity is givern by a(1-e) where t is in s·L4 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 0.6887s1 im...
l 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 a(1-eR) 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 -11.81m/s and b -0.6887s , Part D Find an expression for the distance traveled at time t Express your...
Revieww Correct 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 ▼ Part B 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 11.81m/s and b 0.6887s-1 What was Lewis's acceleration at t 2.10 s? Express your answer using four significant...
l Review What was Lewis's acceleration at t 4.20 s Careful measurements have been made of Olympic sprinters in the 100- Express your answer using four significant figures meter dash. A quite realistic model is that the sprinter's velocity is givern by a(1-e) where t is in s·L4 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 0.6887s1 im...