During the first half of a 3.0 mile bike race with a friend of yours, your frien

Question

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? Correct, computer gets: 705.3 mi/hr^2 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 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)? Answer: Assuming your friend does tie with you at the end. What was her average acceleration over the time interval of the entire race? Answer:

Explanation / Answer

18)

for the first half :

consider my motion :

x = displacement = 1.5 mile

Vo = initial velocity = 0 miles/h

a = acceleration = 705.3 mi/hr2

Vf = final velocity at halfway mark

using the equation

Vf2 = Vo2 + 2 a x

Vf2 = 02 + 2 (705.3) (1.5)

Vf = 46 miles/hr

d = distance remaining to travel = 1.5 miles

t = time taken by me to travel the second half = d/Vf = 1.5/46 = 0.033 hr

for the friend :

V = new speed

d = 1.5 mile

t = 0.033 hr

V = 1.5/0.033 = 46 miles/hr

diference in velocity = 46 - 23 = 23 miles /hr

hence the friend has to travel 23 miles/hr faster

t = time interval = 1.5/23 + 1.5/46 = 0.098 hr

Vo = initial velocity = 23 miles/hr

Vf =final velocity = 46 miles/hr

average acceleration is given as

a = (Vf - Vo)/t = (46 - 23)/0.098 = 234.7 miles/hr2

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