Question

If v( t) represents the velocity of an object and the integral from 0 to 10 v(t) dt =12
Which of the following must be true?
I. There is a displacement of 12 units from t=0 to t=10.
II. The object has traveled a distance of 12 units on the interval 0 is greater than or equal to t is greater than or equal to 10.
III. The position t=10 of the object is 12 units from the origin.

Answer 1

I only
II only
I and III only
I,II, and III

Answer 2

I thought that it was II only

Answer 3

A few hints/questions:

\(\displaystyle \int v(t)~dt=s(t)\), where \(s(t)\) is the displacement. A definite integral would give you the net displacement over some time interval.

The interval you provided in II doesn't seem right. The way it's written tells me \(t\le 0\) and \(t\ge 10\). Did you mean \(0\le t\le10\)?

Displacement \(\not=\) distance.

Displacement \(=\) position.

Answer 4

That is what I meant