Physics Hard question

Question

Imagine that a sprinter accelerates from rest to a maximum speed of 10.8m/s in 1.8s. In what time interval will he finish the 100-m race if he keeps his speed constant at 10.8m/s for the last part of the race? What assumptions did you make?

Answer 1

Technically, we didn't need to assume the sprinter started from rest, since the problem states that directly.  So only the constant or average value for the acceleration needed to be assumed.

Answer 2

Assuming the sprinter starts at rest (speed = 0) and accelerates at a constant rate, his acceleration will be:

 

     a = Δv/Δt = (10.8-0)/(1.8-0) = 10 m/s²

 

The distance he travels while accelerating is:

 

     d = (1/2)at² = (1/2)(10)(1.8²) = 16.2 m

 

The race is 100 m long, so the sprinter must run an additional 100 - 16.2 = 83.8 m at a constant speed of 10.8 m/s.  The time that takes is:

 

     d = v*t

     83.3 = (10.8)t

     83/10.8 = t

     7.76 sec = t

 

So the runner took 1.80 sec to run the first 16.2 m and 7.76 sec to run the last 83.3 m.  Total time= 1.80 + 7.76 = 9.56 sec.  That time would break Usaine Bolt's world record of 9.58 sec!