Suppose that the distance an aircraft travels along a runway befoer takeoff is given by $\displaystyle D=\frac {10t^2}{9}$ , where D is measured in meters from the starting point and t is measured in seconds from that time the brakes are released If the airplane will become airborne when its speed reaches 200 km/h, how long will it take to become airborne, and what distance will it have traveled by that time?

Phew.

Okay, I think

1st find velocity (derivative of distance)

$\displaystyle v(t)= \frac {20t}{9}$

Then set $\displaystyle 200= \frac {20t}{9}$

Then solve for t. T= 90 h

2nd plug 90 for t in the original equation.

and solve for t.

t= 9000 km/h

Yes? NO? Maybe so?

Thank you!