Aeroplane Take-off speed w/ runway length, time, init speed

[charlesmci]

If anyone can help me with this question it would be greatly appreciated:

An air-plane has a runway of 5.76 km, starts with a speed of 4 m/sec and moves with constant acceleration. If the air-plane makes the run in 2 min, with what speed does it take off?

My knowledge of differential equations is fairly basic at this stage and unfortunately this is enough to stump me.

 

[stapel]

An air-plane has a runway of 5.76 km, starts with a speed of 4 m/sec and moves with constant acceleration. If the air-plane makes the run in 2 min, with what speed does it take off?

Can you use what you learned back in calculus?

You have v(0) = 4, s(0) = 0, s(120) = 5.76, and a(t) = c for some constant c. Can you then integrate to get the information you need about v(120)?

 

[charlesmci]

Yeah that was the approach I was thinking of but all we've studied in this course is seperable and exact differential equations so
I assumed they wanted it in that format. Thank you for your help though!

 

[Deleted member 4993]

start with:

\(\displaystyle a \, = \, \frac{dv}{dt} \, = \, \frac{dv}{ds}\cdot \frac{ds}{dt} \, = \, \frac{dv}{ds}\cdot v\)

\(\displaystyle a \, ds = v \, dv\)

\(\displaystyle a \int_0^{s_1}ds = \int_{v_{initial}}^{v_{final}}v \, dv\)

Now apply conditions to solve for ingration limits and integrate ...