Calculus Problem! Its my last one and its really bugging me! Please help. Thanks! :) ?

Question

Okay. I don't know how to solve this. I tried but-- I don't know. So, if you guys could help me that would be super awesome!! THANKS! :)

Here it is:

A modern jet fighter aircraft needs to be traveling at 108 yards/sec down the runway in order to take off. It is known that the jet can accelerate from 0 to 108 yards/sec in 6 seconds (assume constant acceleration).

Determine the shortest length the runway can be if the plane starts from rest at one end and has to take off at least 140 yards before the runway ends?

THANK YOU! :) :)

Answer 1

a = k

v = kt (since v(0) = 0)

s = kt^2/2 (again since s(0) = 0 .. . .)

then we know that v(6) = 108

6k = 108

k = 18

thus

s = 9t^2

s(6) = 324 (this is the length the fighter travels before reaching 108 yd/sec)

thus the runway has to be

324 + 140 = 464 yards

.. . .. .