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**Question:**A web page designer creates an animation in which a dot on a computer screen has a position of r=[4.0 cm + (2.5 cm/s

^{2})t

^{2})i + [(5.0 cm/s)t]j.

a. Find the magnitude and direction of the dot's average velocity between t=0 and t=2.0s.

b. Find the magnitude and direction of the instantaneous velocity at t=0, t=1.0s, and t=2.0s.

## Homework Equations

r=[4.0 cm + (2.5 cm/s

^{2})t

^{2})i + [(5.0 cm/s)t]j.

## The Attempt at a Solution

For part A, I had no problem. I found the position at t=0 and t=2 and used the distance formula to find the resultant. I divided that by the time interval, 2 seconds, and got an average velocity of 7.07 m/s at a 45 degree angle. When I checked this with the back of my book, my answer was correct.

For part B, I figured that I would take the derivative of the given equation, which is what I did.

r=(4.0 + 2.5t

^{2})+5t

r'=5t + 5

I'm already unsure about this step; I'm not quite sure what the I and J indicate in the original equation. I thought they meant X and Y, so I also tried splitting up the formula into an x-component and a y-component, but I still did not get the right answer.

For t=0, the answer was 5.0 cm/s, which I think I got just by sheer luck and coincidence. So really, I don't even know how to approach part B of this problem...the answer for t=1.0s is supposed to be 7.1 cm/s...help?