# Integral for displacement from velocity

1. Jan 29, 2013

### burton95

1. The problem statement, all variables and given/known data
An object is moving with a velocity by the equation

v(t) = [(3/2)(m/s2)t] i^ + [(3/2)(m/s3)t2] j^

What is the magnitude of displacement during 0 - 2s

2. Relevant equations

v(t) = [(3/2)(m/s2)t] i^ + [(3/2)(m/s3)t2] j^

3. The attempt at a solution

(3/2) ∫ from 0 to 2 [(t2 / 2) i^] + [t3/3]y^

plug and chug with t = 2

(3/2) √(squaring each of the i^ + j^)

I end up with some decimal answer which I know is wrong. Where am I screwing up?

2. Jan 29, 2013

### Staff: Mentor

Who says you're wrong. What do you get? Is it something like 6.5?

3. Jan 30, 2013

### burton95

When I plug in 6.5 to the online quiz it says sorry wrong answer, "Don't forget to add the components of a vector quadratically to determine it's magnitude." I don't understand where I'm going wrong. Help

Last edited: Jan 30, 2013
4. Jan 30, 2013

### burton95

wait what about the units of s^2 and s^3????

EDIT: I don't think that's it

Last edited: Jan 30, 2013
5. Jan 30, 2013

### Staff: Mentor

Oops. 6.5 was wrong. I must have made a mistake somewhere. Here are the correct results: What did you get for the two components of the displacement vector? I got 3 and 4 using your equation. They were 3/2 x 2, and 3/2 x 8/3. So the correct displacement magnitude must be 5.

Sorry for any confusion I caused. It looks like you had it right all the way, but just made a mistake in arithmetic.

Chet