Posted by **D** on Thursday, November 11, 2010 at 5:13pm.

A particle moves in a straight line with velocity t^-2 - 1/9 ft/s. Find the total displacement and total distance traveled over the time interval [1,4].

I found out that the total displacement is .4116

But I cannot find the total distance traveled.

- Calculus -
**MathMate**, Thursday, November 11, 2010 at 5:51pm
Let

v(t)=velocity function = t^-2 - 1/9

s(t)=displacement function. = -t/9-1/t

and

displacement = s(4)-s(1)= -25/36 - (-10/9) = 5/12 ft.

If s(t) is monotonically increasing or decreasing, then the displacement equals the distance travelled.

However, we note that v(3)=0, after which time the velocity reverses in direction.

So the distance travelled equals

s(4)-s(3) - [s(3)-s(1)]

=-25/36 -(-2/3) - [(-2/3)-(-10/9)]

=-17/36

Ignore the sign, since distance is a scalar.

So distance = 17/36 ft.

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