velocity calculus problem

[killasnake]

This is my first year taking calculus and I'm a little lost already. Can you help me with this problem?

A steam catapult aboard an aircraft carrier can accelerate an F-18 Hornet so that its velocity is given by:

v(t) = 104.85t feet/second

If the jet reaches its take-off velocity of 173 miles per hour at the end of the runway, how long does it take, in seconds, for the jet to take off? How long is the runway (in feet)?

How would I solve this problem?

 

[stapel]

Convert "173 mph" into the equivalent "feet per second" (fps).

Once you have the ending velocity in fps, set the "velocity" equation equal to this value. Solve for the time t in seconds.

Note that the position function, s(t), is the integral of the velocity function. Assuming you start counting when the catapult starts, so v(0) = 0 and s(0) = 0, integrate v(t) and then evaluate that the time value you found for the first part of the question.

Eliz.

 

[killasnake]

What I came up with then I converted it to fps is

173mph to 253.7333 fps

Once you have the ending velocity in fps, set the "velocity" equation equal to this value. Solve for the time t in seconds.

How do I solve for t?

 

[Gene]

To solve for t:
You know
v(t) = 104.85t feet/second
so
253.7333 = 104.85 * t

t = 253.7333 / 104.85

 

[galactus]

Hello Gene. Welcome back!