How do I calculate the distance traveled by an airplane flying into a headwind?

[leroyjenkens]

Homework Statement

The velocity of an airplane flying into a headwind is given by v(t) = 30(16 - t^2) mi/hr for 0 < t < 3 hr.
How far has the airplane traveled at the instant its velocity reaches 400 mi/hr?

Assume s(0) = 0

The Attempt at a Solution

I think I would have to find the area under the graph. So basically I have a velocity time graph? So my objective is to find the area under the graph between time 0 and the time where the plane reaches 400 mi/hr.

I tried setting the velocity equation equal to 400 and solving for t, which would give me the time at which the velocity is 400 mi/hr, right? Well that didn't give me the answer that was in the book. What do you think?

Thanks.

 

[Delphi51]

The approach looks good. I get about 700 miles. I used integration to get the area accurately. If you would like a critique of your calc, share the details.