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## Homework Statement

The position of a particle in meters moving along the x-axis is given by: x=21+22t-6t^2

Calculate the average velocity of the object in m/s during the time interval t=1s to t=3s.

## Homework Equations

x=21+22t-6t^2

t=3 ; t=1

v avg. = Xf - Xi/Tf - Ti = Δx/Δt

don't know if this applies but:

instantaneous velocity = dx/dt = -12t+22

## The Attempt at a Solution

Hello all. I am a returning student with a Major in Civil Engineering. At the age of 35, it is difficult to remember sometimes what the simple answers are. I know this may seem elementary to some of you but I believe I am over thinking this question. Please help.

My question is which answer is correct for the question asked?

I attempted this 2 different ways and can't decide if one of them is correct or if either of them are correct.

substituting:

x=21+22(3)-6(3)^2

x=33m

x=21+22(1)-6(1)^2

x=37m

then 33-37/3-1 = -2 m/s for velocity avg.

speed = absolute value of velocity = 2 m/s

or

I took the derivative of the initial equation and then substituted to get:

v=-12t+22

v=-12(3)+22=-14

v=-12(1)+22=10

then -14-10/3-1=-12m/s = 12m/s

Any help would be great. Thank you.