Question about physics?

Question

I know that it is generally frowned upon to paste a question from an assignment from school here, but, given my 2 day experience in the topic of physics, I find this problem too difficult to answer. It is: Usain Bolt ran 100m in 9.69s. Suppose he reaches his peak velocity at exactly 3.0 seconds and maintains this velocity for the remainder of the race. Find his peak velocity and initial acceleration.

Note: answers are vpeak = 12.21m/s, ainitial = 4.07 m/s^2

Considering the teacher has given us the answers, I assume it would not be a serious offense to attempt to find the process of solving on this site.

Answer 1

The first working formula is

X = VoT + (1/2)aT^2

where

X = distance runner has done in the first 3 seconds

Vo = initial velocity= 0 (since runner starts from rest)

a = runner's acceleration

T = time interval = 3 sec (given)

Substituting values,

X = 0 + (1/2)(a)(3^2)

X = 4.5a  --- call this Equation 1

After negotiating this "X" distance, then the rest of the race was ran in

(100 - X) = V(9.69 - 3)

100 - X = 6.69V

X = 100 - 6.69V --- call this Equation 2

where

V = peak velocity of runner

Since X = 4.5a (from Equation 1), substitute this in Equation 2, i.e.,

4.5a = 100 - 6.69V--- call this Equation 3

The next working formula is

V - Vo = aT (all the terms have been previously defined already) hence, substituting values,

V = a(3) = 3a  --- substituting this into Equation 3,

4.5a = 100 - 6.69(3a) = 100 - 20.07a

Combining terms,

20.07a + 4.5a = 100

24.57a = 100

a = 4.07 m/sec^2

Since V = 3a then,

V = 3(4.07) = 12.21 m/sec.

Hope this helps.

Answer 2

It is a serious offense because the teacher has given you the answers so that you can check that your way is right. That being said, solving this uses d = 1/2at^2 and d = vt, setting the first t to 3s, and the second t to 6.69s. and d1 + d2 = 100m. Work out the rest on your own.