In a women\'s 100-m race, accelerating uniformly, Laura takes 1.90 s and Healan

Question

In a women's 100-m race, accelerating uniformly, Laura takes 1.90 s and Healan 3.15 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 6.40-s mark, and by how much?

---Select--- Laura Healan is ahead by ___ m.

(d) What is the maximum distance by which Healan is behind Laura?
___ m

At what time does that occur?
__ s

Explanation / Answer

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

In a women's 100-m race, accelerating uniformly, Laura takes 2.14 s and Healan 3.36 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 6.20-s mark, and by how much?

is ahead by m.

(d) What is the maximum distance by which Healan is behind Laura?
m

At what time does that occur?
s

Answer

max speeds :-

laura:-

v1 = 100/9.33

v1 = 10.718 m/s

so, acceleration, a1 = v1/2.14 = 5.008 m/s^2

healan:-

v2 = 100/8.72

v2 = 11.468 m/s

so, acceleration, a2 = v2/3.36 = 3.413 m/s^2

(c)

at 6.20:-

laura: 59.09052 m

healen : 51.83536 m

so,

laura is ahead

(d)

laura: distance covered in time t: s1 = 22.1836t - 22.93652

healen: distance covered in time t: s2 = 30.73424t - 38.53248

so, diff = s1 - s2

for, max, differentiate with respect to t

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