# Calculus

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A fully plane has a constant acceleration while moving down a runaway. the plane requires .7 mile of runaway and a speed of 160 miles per hour in order to lift off. what is the planes accelearation?

i need the formula cause the one i have doesnt work cause i need time

• Calculus -

vel = at where t is in hrs, and a is in miles/hrs^2
then s = (1/2)at^2 where s is the distance in miles

when v = 160
at=160
t = 160/a

when s= .7
(1/2)a(160/a)^2 = .7
a = 18285.7 miles/hrs^2

so what time is liftoff?

160 = 18285t
t = .00875 hrs or 31.5 seconds

check:
at t= 0,
v = 0
s = 0

when t = .00875
v = 18285.7(.00875) = 160
s = (1/2)(18285.7)(.00875)^2 = .699999

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