17) During the first half of a 3.0 mile bike race with a friend of yours, your f

Question

17) During the first half of a 3.0 mile bike race with a friend of yours, your friend bikes the whole way at a constant speed of 23 mi/hr. You start from rest and accelerate constantly from the beginning. You both are neck-and-neck at the half-way point of the race. What was your acceleration rate?

18) For the second half of the race, you maintain the same speed you had at the half-way point. How much faster does your friend need to bike to tie with you at the end of the race (assume that they pick up their pace very quickly and so you can think of them as moving at a constant speed for pretty much the entire second half of the race)?

19) Assuming your friend does tie with you at the end. What was her average acceleration over the time interval of the entire race?

Explanation / Answer

3 mile = 4828.03 m

23 mi/hr = 10.2819 m/s

time taken by friend at half point = 4828.03/2*10.2819 = 234.78 s

now you start from rest and accelerate constantly

s = ut + 1/2 * at^2

s = half way = 4828.03/2

t = 234.78 s

u = 0 start from rest

s = 1/2 * a*t^2

a = 2s/t^2

a = 0.088 m/s^2

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