Calculus Question:
If the velocity of a particle moving along the x-axis is given by v(t)=3t^2+2 and initially it is 4 units to the left, find the position equation x(t).

Question

Calculus Question:
If the velocity of a particle moving along the x-axis is given by v(t)=3t^2+2 and initially it is 4 units to the left, find the position equation x(t).

moonlight10198 · Answer

Mostly I want to know how having the particle 4 units to the left will effect this question.

solomonzelman · Answer

$\large\color{slate}{ v(t)=3t^2+2            }$  is same as,  $\large\color{slate}{ s'(t)=3t^2+2            }$

saying, vecloty function, is a derivative of the position function.

solomonzelman · Answer

you have to find the position function $\large\color{slate}{ s(t)           }$, and for that you would need to find the anti-derivative/integral.

moonlight10198 · Answer

I know how to do that, but how do the four units factor into that? Does C=4 since it was originally 4 units to the left?

moonlight10198 · Answer

or C=-4

solomonzelman · Answer

oh, s(t) is x(t).... but you get the point.

solomonzelman · Answer

always disconnect on here sorry

moonlight10198 · Answer

that's fine

moonlight10198 · Answer

would this make sense though?

solomonzelman · Answer

the particle is initially 4 units to the left, means that   $\large\color{slate}{ x(0)=-4            }$

solomonzelman · Answer

So, C is -4  (i think)

moonlight10198 · Answer

oh I see now

solomonzelman · Answer

yes, so what is you position function?

moonlight10198 · Answer

x(t)=t^3+2t-4

solomonzelman · Answer

:)

solomonzelman · Answer

don't know why x(t) and not s(t)  (that is typical), but yes, correct and well done.

moonlight10198 · Answer

Yeah we use x(t)
Thank you for the help :D

solomonzelman · Answer

yw