yes, it is. object moves right at 1 mps for five seconds. Graph it. Displacement is 5 m. Area of graph is five meters. Same object reverses direction and moves at 1 mps for ten seconds. Total displacement is 5 m + -10 m = -5 m. Graph it. Area above the x-axis is 5 m, area below is 10 m, or -10 m for the purposes of the calcultion.

 

This is true. The area is positive. The integral is -10 m, which is what you use to determine the total displacement. The area gives you the total motion that results in that displacement: 5 + 10 = 15 meters.

Area is nonnegative.

 

Before or after it takes off?

 

no but i can turn it up to 11.

 

That's 1 louder.

 

Well, you see...the negative volume below the wheels creates a black hole which in turn prevents the plane from taking off. It also boils all cold water that it comes across on the runway and instantly freezes any hot water that it comes across

 

[QUOTE=no_really,Dec 5 2005, 11:44 AM] yes, it is.

 

If you drive an H2 5 miles East, then turn around and drive it 10 miles West, your displacement from your starting point is 5 miles (West), but you've still used 5 gallons of gas (15 mi. @ 3 mpg), not 5/3 gallons.

 

YOu can have what is referred to as a signed area, but it's actually the result of multiplying a scalar area with a unit normal vector. It's then not technically an area, though it may just be called the "area". Just as speed is a positive scalar, which is the magnitude of velocity, which is a vector (meaning it can be negative). I think I've got my wording correct. In engineering, we never worried about the math too much, as long as we understood the answer it helped us arrive at

 

WHAT?

You tell me: which of these is "negative": 3i - 4j, -3i + 4j. (They're additive inverses, so if "negative" has any meaning at all for vectors, then exactly one of these must be "negative" and the other "positive".)