Question

A particle is moving with the given data. Find the position of particle.
a(t)=t^2-4t+6, s(0)=0, s(1)=20

Answer 1

I assume you want to find s as a function of t where s is your position function?

Generally a represents your acceleration function, so if you integrate a you will get v(t) (the velocity function). Don't forget about adding your constant of integration!

Then if you integrate v(t) you will get s(t) with a second constant of integration.

At that point you just plug in your initial values in order to find out what the two constants of integration are.

I'll stick around in case you need help with any of the steps.

Answer 2

This is exactly what I want to find. I was actually wondering if my answer was correct, but I'll just throw out the key parts of it. To find v(t) I found the anti derivative of a(t), which is t^3/3 - 4t^2/2 + 6t + c. Is that correct? And from there, s(t) would equal t^4/4 - 2t^3/3 + 6t^2/2 + Cx + D?

Answer 3

Your v(t) is correct. There is a problem with your s(t) though.

\[\int\limits_{}^{} \frac{ t ^{3} }{ 3 }dt \neq \frac{ t ^{4} }{ 4 }\] (you forgot your factor of 1/3).

Other than that just simplify and then plug in your initial values.

Answer 4

Ah, so it would be t^4/12?

Answer 5

Yep!

Answer 6

Awesome, thanks! :)