# Find the antiderivative of the following vector:

## Homework Statement

Calculate the position vector of a particle moving with velocity given by:

v = (32 m/s - (5 m/s^2 )t i) + (0 j)

## Homework Equations

(x^(n+1) / (n+1) ) + C = antiderivative of function

## The Attempt at a Solution

r = (32t m - (5/2)t^2 m/s + C m i) + (C j)

Honestly, I'm just confused with the units more than anything. I don't know why the problem has m/s^2 if it's a velocity vector...

SteamKing
Staff Emeritus
Homework Helper

## Homework Statement

Calculate the position vector of a particle moving with velocity given by:

v = (32 m/s - (5 m/s^2 )t i) + (0 j)

## Homework Equations

(x^(n+1) / (n+1) ) + C = antiderivative of function

## The Attempt at a Solution

r = (32t m - (5/2)t^2 m/s + C m i) + (C j)

Honestly, I'm just confused with the units more than anything. I don't know why the problem has m/s^2 if it's a velocity vector...

A quantity of 5 m/s2 indicates that accelerated motion is taking place, i.e., the velocity is changing w.r.t. time. Acceleration × time = change in velocity.

A quantity of 5 m/s2 indicates that accelerated motion is taking place, i.e., the velocity is changing w.r.t. time. Acceleration × time = change in velocity.

oooooh okay that makes more sense. thank you!

and the antiderivative is right, right?

SteamKing
Staff Emeritus
Homework Helper
oooooh okay that makes more sense. thank you!

and the antiderivative is right, right?
I would say that since the velocity vector had no j-component, the position vector will not either.

I would say that since the velocity vector had no j-component, the position vector will not either.
but isn't the antiderivative of 0 C (or in this case, D to differentiate)?

SteamKing
Staff Emeritus
Homework Helper
but isn't the antiderivative of 0 C (or in this case, D to differentiate)?
Yeah, but D = 0 would be an acceptable value for the constant of integration, in the absence of any other initial condition information.

Yeah, but D = 0 would be an acceptable value for the constant of integration, in the absence of any other initial condition information.

oh okay. since this is on a take home test, do you think I should just put both answers (one for a definite integral 0 and one for an indefinite integral D)?

SteamKing
Staff Emeritus