Physics - Horizontal Kinematics question?!?

Question

A Cessna 150 aircraft has a lift-off speed of

approximately 125 km/h.

What minimum constant acceleration does

this require if the aircraft is to be airborne

after a take-off run of 131 m? Answer in units

of m/s2.

What is the corresponding take-off time? An-

swer in units of s.

If the aircraft continues to accelerate at this

rate, what speed will it reach 24.8 s after it

begins to roll? Answer in units of m/s.

I got the answers to the first two parts correct but I cannot figure out the third one! Please show me how you've worked it out! :) Thanks.

Answer 1

Let:

u be initial speed,

v be final speed,

a be acceleration,

t be time,

s be distance.

125 km/hr = 125 * 10^3 / 3600 = 34.7222 m/s.

v^2 = u^2 + 2as

a = (v^2 - u^2) / (2s)

= (34.7222^2 - 0) / (2 * 131)

= 4.60 m/s^2.

s = t(u + v) / 2

t = 2s / (u + v)

= 2 * 131 / (0 + 34.7222)

= 7.55 s.

v = u + at

= 0 + 4.60 * 24.8

= 114 m/s.