acceleration question

**cinder** · September 10th 2007, 06:26 PM

I know the answer to the following problem is $32m/s^2$ , but I don't see how it is obtained if you're not given $t$ (time).

The catapult of the aircraft carrier USS Abraham Lincoln accelerates an F/A-18 Hornet jet fighter from rest to a takeoff speed of $173 {\rm mi/h}$ in a distance of $307 {\rm ft}$ . Assume constant acceleration.

After it gave me the answer, I was then able to figure out $t$ .

**cinder** · September 10th 2007, 06:31 PM

I figured it out. I missed that problem... should have just kept at it.

$v^2_x=v^2_{0x}+2a_x(x-x_0)$

**topsquark** · September 10th 2007, 07:40 PM

Originally Posted by cinder

I know the answer to the following problem is $32m/s^2$ , but I don't see how it is obtained if you're not given $t$ (time).

The catapult of the aircraft carrier USS Abraham Lincoln accelerates an F/A-18 Hornet jet fighter from rest to a takeoff speed of $173 {\rm mi/h}$ in a distance of $307 {\rm ft}$ . Assume constant acceleration.

After it gave me the answer, I was then able to figure out $t$ .

Originally Posted by cinder

I figured it out. I missed that problem... should have just kept at it.

$v^2_x=v^2_{0x}+2a_x(x-x_0)$

That equation will give you the acceleration of the Hornet (presuming you do the unit conversions correctly.)

If you wanted the time it takes the catapult to move the Hornet the 307 ft, you can use
$x = x_0 + \frac{1}{2}(v_0 + v)t$

This equation is often skipped over in classes, but is nothing more than
$x = x_0 + \bar{v}t$
(where $\bar{v}$ is the average speed) when the acceleration is constant. I find it comes in handy every now and again.

-Dan

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