Answer:
It will take 90s for the aircraft to become airbone.
In that time, the aircraft will have traveled 13500m = 13.5km.
Step-by-step explanation:
The velocity function is the derivative of the distance function.
In this problem, we have the following distance function:
[tex]D(t) = \frac{5t^{2}}{3}[/tex]
So the speed function is the following:
[tex]S(t) = \frac{10t}{3}[/tex]
The aircraft will become airborne when its speed reaches 300km/h. How long will it take to become airborne?
This is going to happen when S(t) = 300. So:
[tex]S(t) = \frac{10t}{3}[/tex]
[tex]\frac{10t}{3} = 300[/tex]
[tex]t = 90[/tex]
It will take 90s for the aircraft to become airbone.
What distance will it travel in that time?
This is D(t) when t = 90. So:
[tex]D(t) = \frac{5t^{2}}{3}[/tex]
[tex]D(90) = \frac{5*90^{2}}{3} = 13500[/tex]
In that time, the aircraft will have traveled 13500m = 13.5km.
