Chapter 02, Problem 111 A certain sprinter has a top speed of 9.86 m/s. If the s

Question

Chapter 02, Problem 111 A certain sprinter has a top speed of 9.86 m/s. If the sprinter starts from rest and accelerates at a constant rate, he is able to reach his top speed in a distance of 10.2 m. He is then able to maintain his top speed for the remainder of a 100 m race. (a) What is his time for the 100 m race? (b) In order to improve his time, the sprinter tries to decrease the distance required for him to reach his top speed. What must this distance be if he is to achieve a time of 11.0 s for the race?

Explanation / Answer

Here ,

top speed , v = 9.86 m/s

d1 = 10.2 m

a) let the acceleration is a

Using third equation of motion

v^2 - u^2 = 2 *a * d1

9.86^2 = 2 * 10.2 * a

a = 4.77 m/s^2

Now , for the total time taken

total time taken = (9.86)/(4.77) + (100 - 10.2)/9.86

total time taken = 11.2 s

the total time taken is 11.2 s

b)

let the acceleration needed is a

and time of acceleration is t

Now, for the distance

using second equation of motion

d = 0.50 * a * t^2

1st equation of motion

9.86 = a * t

for total time

11 = 9.86/(a) + (100 - d)/9.86

solving these equations

d = 8.46 m

he should reach the top speed is 8.46 m

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