# Find the antiderivative of the following vector:

1. Oct 14, 2015

### brinstar

1. The problem statement, all variables and given/known data
Calculate the position vector of a particle moving with velocity given by:

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

2. Relevant equations

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

3. 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...

2. Oct 14, 2015

### SteamKing

Staff Emeritus
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.

3. Oct 14, 2015

### brinstar

oooooh okay that makes more sense. thank you!

and the antiderivative is right, right?

4. Oct 14, 2015

### SteamKing

Staff Emeritus
I would say that since the velocity vector had no j-component, the position vector will not either.

5. Oct 14, 2015

### brinstar

but isn't the antiderivative of 0 C (or in this case, D to differentiate)?

6. Oct 14, 2015

### SteamKing

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

7. Oct 14, 2015

### brinstar

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)?

8. Oct 15, 2015

### SteamKing

Staff Emeritus
You can have a definite integral only if you know the value of t.

9. Oct 15, 2015

### brinstar

hmm... so what should I put down?