A world-class sprinter can burst out of the blocks to essentially top speed (of about 11.5 m/s) in the first 15.0 m of the race. what is the average acceleration of this sprinter, and how long does it take her to reach that speed?

Given:

u = 0, initial speed (sprinter starts from rest)

v = 11.5 m/s, final speed

s = 15 m, distance traveled to attain final speed.

Let

a = average acceleration,

t = time taken to attain final speed.

Then

v² = u² + 2as

or

(11.5 m/s) ² = 2 * (a m/s²) * (15 m)

a = 11.5² / (2*15) = 4.408 m/s²

Also

v = u + a t

or

(11.5 m/s) = (4.408 m/s²) * (t s)

t = 11.5/4.408 = 2.609 s

Answer:

The average acceleration is 4.41 m/s² (nearest hundredth).

The time required is 2.61 s (nearest hundredth).