In a women\'s 100-m race, accelerating uniformly, Laura takes 1.95 s and Healan

Question

In a women's 100-m race, accelerating uniformly, Laura takes 1.95 s and Healan 3.04 s to attain their maximum speeds, which they each maintain for the rest of the race. They cross the finish line simultaneously, both setting a world record of 10.4 s.

(a) What is the acceleration of each sprinter?

(b) What are their respective maximum speeds

(c) Which sprinter is ahead at the 6.35-s mark, and by how much?

Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m.

Explanation / Answer

a and b)
for Laura:
Vmax = Vi+a*t1= a*t1 = a*1.95
Total distance = 0.5*a*t1^2 + Vmax* (t2-t1)
=0.5*a*1.95^2 + Vmax * (10.4-1.95)
= 0.5*a*1.95^2 + a*1.95 * (10.4-1.95)
= 1.9 a + 16.48a
100 = 18.38 a
a = 5.44 m/s^2
Vmax = a*1.95 = 5.44*2.1.95 = 10.6 m/s

for healen:
Vmax = Vi+a*t1= a*t1 = a*3.04
Total distance = 0.5*a*t1^2 + Vmax* (t2-t1)
=0.5*a*3.04^2 + Vmax * (10.4-3.04)
= 0.5*a*3.04^2 + a*3.04 * (10.4-3.04)
= 4.62 a + 22.37a
100 = 26.99 a
a = 3.7 m/s^2
Vmax = a*3.04 = 3.7*3.04 = 11.26 m/s

C)

At 6.35 s s
d of Laura = 0.5*a*t1^2 + Vmax* (t2-t1)
=0.5*5.44*1.95^2 + 10.6 * (6.35-1.95)
= 57 m
d of Haelen = 0.5*a*t1^2 + Vmax* (t2-t1)
=0.5*3.7*3.04^2 + 11.26* (5.65-3.04)
= 46 .5 m
Laura is ahead by (57-46.5) = 10.5 m

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