In a women\'s 100-m race, accelerating uniformly, Laura takes 2.00 s and Healan

Question

In a women's 100-m race, accelerating uniformly, Laura takes 2.00 s and Healan 3.00 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 respectve maximum speeds? (c) Which sprinter is ahead at 6.00-s mark, and by how much? (d) What is the maximum distance by which Helean is behind Laura, and at what time does that occur?

The correct answers are (a) 5.32 m/seconds squared for Laura and 3.75 m/seconds squared for Healan (b) 10.6 m/s for Laura and 11.2 m/s for Healan (c) Laura, by 2.63 m (d) 4.47 m at t = 2.84 s

How do I obtain these answers?

Explanation / Answer

First deal with Laura:
She ran 10.4-2.0 = 8.4 sec running at constant speed Call this constant speed L m/s
The distance she ran at velocity L m/s = time * velocity = 8.4L m
Calculate her acceleration
V = U +at
L = 0 + a*2
a = L/2m/s²

Calculate the distance taken to achieve max velocity, Lm/s
s = ut + 0.5*at²
s = 0 + 0.5*(L/2) * 2²
s = L metres

8.4L + L = 100
L = 100/9.4
L = 10.64 m/s velocity
She accelerated from rest to max velocity of 10.64m/s in 2 seconds
Calculate acceleration:
v = u+at
10.64 = 0 + 2a
a = 5.32m/s²

That seems to work out OK for Laura, so we do the same for Healan

She ran 10.4-3.0 = 7.4 sec running at constant speed Call this constant speed H m/s
The distance she ran at velocity H m/s = time * velocity = 7.4H m
Calculate her acceleration to reach V=Hm/s in 3 seconds
V = U +at
H = 0 + a*3
a = H/3 m/s²

Calculate the distance taken to achieve max velocity, Hm/s
s = ut + 0.5*at²
s = 0 + 0.5*(H/3) * 3²
s = 1.5H metres

7.4H + 1.5H = 100
H = 100/8.9
H = 11.23 m/s is the max velocity

She accelerated from rest to max velocity of 11.23m/s in 3 seconds
Calculate acceleration:
v = u +at
11.23 = 0 + 3a
a = 11.23/3
a = 3.74 m/s²

Final answer: Laura's acceleration = 5.32m/s squared
Healan's aceleration= 3.74m/s squared

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