Question

An airplane needs at least 145 meters of runway to take off. If the plane starts from rest and accelerates uniformly to a take-off speed of 170 km/hr then what is its acceleration in meters/second? How long does it take for the plane to become airborne?

Answer 1

First, get everything in the same units. The answer must be in m/sec^2, so we need to convert 170 km/hr to m/sec.

170 km/hr * 1000m/km * hr/3600sec = 47.222m/sec

Now, we know that it takes some time, t, to take off.

v = at
47.222 = at, so
t = 47.222/a

Distance s = 1/2 at^2
145 = 1/2 a (47.222/a)^2 = 2229.938/2a
290a = 2229.938
a = 7.69 m/sec^2

So, checking our answer

t = 47.222/7.69 = 6.14 sec

s = 1/2 * 7.69 * 6.14^2 = 144.955 m

Close enough for jazz.