Calculating Velocity of a Cannonball After Varying Force

[Cherrybawls]

Homework Statement

A .8kg cannon ball is shot out of a cannon with force 2000-100,000t. When the ball leaves the cannon, the force is zero. What is the velocity of the ball as it leaves the cannon.

Although the problem doesn't specify, I assume there is no gravity or any other external forces since there is no angle of the force or cannon given.

Homework Equations

F=ma
Unfortunately, I have not learned how to solve equations dealing with varying acceleration, so I don't really know what to do...

The Attempt at a Solution

I found that the cannon ball leaves the cannon at t=.02, but I don't know what to do once I have that to find the final velocity...

 

[cepheid]

Hi Cherrybawls, welcome to PF!

Unfortunately, I have not learned how to solve equations dealing with varying acceleration, so I don't really know what to do...

The easiest way to do it is to integrate the a(t) function (acceleration as a function of time) in order to get the final velocity:

$$v(0.02) - v(0) = \int_0^{0.02} a(t)\, dt$$​

If you haven't done any calculus, then the above will probably not mean much to you. However, another method, which is *entirely equivalent* is to compute the area underneath the a vs. t graph, over that time interval. That will give you the change in velocity over that time interval. In this case, I think we can assume that the initial velocity, v(0), is 0, so that the change in velocity is just equal to the final velocity achieved.

 

[Cherrybawls]

Well, I am learning calculus now, but we have not yet gotten to integrals so I will go ahead and try the second method you mentioned, thank you so much