Question

One simple model for a person running the 100 m dash is to assume the sprinter runs with constant acceleration until reaching top speed, then maintains that speed through the finish line.
If a sprinter reaches his top speed of 10.8 m/s in 2.54 s, what will be his total time?

Answer 1

While accelerating, he runs 5.4*2.54 = 13.72 meters. (The average speed is half the maximum).
That leaves 86.28 m still to be run at 10.8 m/s. That will take 10.8/10.8 = 7.99 s.

The total time for the 100 meters is
7.99 + 2.54 = 10.53 s

Answer 2

SOLUTION :

Initial speed = 0 m/s

Top speed  = 10.8 m/s 

As top speed is attained at constant acceleration, we can consider average speed 

during the acceleration period to determine the distance run.

So, 

Distance run in the acceleration period

= average speed * time taken

= (0 + 10.8 / 2 * 2.54

= 5.4 * 2.54

= 13.716  m 

So, distance run at top speed of 10.8 m/s 

= 100 - 13.716

= 86. 284 m 

Time taken to `run at constant top speed

= Distance run / top sped

= 86.284 / 10.8

= 7.99 sec

Total time taken to run 100m race

= time at constant acceleration + time at constant sped

= 2.54 + 7.99

= 10.53 sec (ANSWER).