Question

A world-class sprinter accelerates to his maximum speed in 3.8 s . He then maintains this speed for the remainder of a 100-m race, finishing with a total time of 9.3 s .

What is the runner's average acceleration during the first 3.8 s ?

What is his average acceleration during the last 5.5 s ?

What is his average acceleration for the entire race?

Answer 1

1)

let the acceleration be a and final velocity be v

then for 1st 3.8 s:

vf = vi + a*t

v = 0 + a*3.8

v = 3.8*a

distance travelled in this time:

d1 = vi*t + 0.5*a*t^2

= 0 + 0.5*a*(3.8)^2

= 7.22*a

for remaining time:

velocity = v

distance = 100 - d1

= 100 - 7.22*a

time= 9.3 s - 3.8 s

= 5.5 s

use:

distance = speed * time

100 - 7.22*a = v*5.5

100 - 7.22*a = 7.22*a*5.5

100 - 7.22*a = 39.71*a

46.93*a = 100

a = 2.13 m/s^2

Answer: 2.13 m/s^2

2)

since velocity is constant during last 5.5 s

average acceleration = 0

Answer: 0 m/s^2

3)

initial velocity = 0 m/s

final velocity = 3.8*a

= 3.8*2.13 m/s^2

= 8.094 m/s

average acceleration = change in velocity / change in time

= (8.094 - 0 ) m/s / 9.3 s

= 0.870 m/s^2

Answer: 0.870 m/s^2