Displacement (Answer Key Error)

[Qube]

Homework Statement

The position of an object traveling in a straight line at time t is given by s(t) = (2/3)t^2 + 4t^2 + 6t + 2.

What's the displacement after 3 seconds?

Homework Equations

Displacement is final position minus initial position.

The Attempt at a Solution

Displacement at 3 seconds is s(3) - s(0).

s(0) = 2. Note the constant term!

s(3) = 18 - 36 + 18 + 2.

s(3) - s(0) = 0.

Interestingly enough, my key claims displacement is simply s(3).

I'm guessing this is an error (and not on my part)!

 

[AATroop]

Can you explain how 2/3 * t^2 = 4*t^2 + 6*t + 2?

 

[Qube]

Sorry, replace the second equal sign with a plus sign. I've corrected it in the OP.

 

[AATroop]

OK, can you also show how you're getting s(3)? Because, if the equation is s(t) = (2/3)t^2 + 4t^2 + 6t + 2, then at t = 3, the current position is 6 + 36 + 18 + 2. Which is equal to 62. If the equation is s(t) = (2/3)t^2 - 4t^2 + 6t + 2, then at t = 3, the current position is 6 - 36 + 18 + 2, which is equal to -10. Not sure if you're copying the equation wrong or what...

 

[Qube]

I think I did copy the problem wrong, but I know there was a constant at the end, which makes the answer key unequivocally wrong, correct?

 

[Qube]

Okay, I found it!

http://i.minus.com/jW4oBtV2mWi3O.png

http://i.minus.com/jbrSQnX1kxCiGG.png

 

[AATroop]

Well, it definitely seems like now there is an error in the answer key. So, yes, I would not follow it.