During the first half of a 2.0 mile bike race with a friend of yours, your frien

Question

During the first half of a 2.0 mile bike race with a friend of yours, your friend bikes the whole way at a constant speed of 20mi/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? 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 in order to tie with you at the end of the race (assume heat 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)? 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

(17)let t= time taken for first half of the race

time taken by friend= t= 1 mile/20 mi/hr = 0.05 hr

for you, initial velocity=0 ,distance= 1 mile

we use kinematic equation x= vi t + 1/2 a t^2

1= 0(t)+ 0.5(a)(0.05)^2

a= 800 mi/hr^2 .

(b) for your speed half way, we use kinematic equation; Vf= vi + a t

Vf= 0+ 800(0.05)=40 mi/hr

so time taken by me in second half= 1 mile/40 mi/hr= 0.025 hr

so speed of friend= distance/ time= 1 mi/0.025hr = 40 mi hr

so speed of friend has to be 40 mi /hr insecond half to finish with you.

(c) acceleration of friend= (Vf-vi)/t

a= (40-20)/(0.05+0.025)

a=266.7 mi/hr^2

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