Anette is a civil engineer and needs to determine the length of a highway on-ram

Question

Anette is a civil engineer and needs to determine the length of a highway on-ramp before construction begins. If the average vehicle takes 10.8 seconds to go from 20.0 mi/h to 60.0 mi/h, how long should she design the seperate merge lane to be so a car can reach a speed of 60.0 mi/h before merging?

I really want to understand how to do this problem, so if you could show your work that would be wonderful! Thank you! In the back of the book the answer reads 633 feet, but I have no idea how to get to that answer.

Explanation / Answer

t = 10.8 sec = 3x 10-3 h

a = 60 - 20/t   =13333.33 mi/h^2

2as = v^2 - u^2

2 x 13333.33 x s = 60^2 - 20^2  

s = 0.12 mi

1 mile = 5280 feet

so s = 0.12 x 5280 = 633.60 feet

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