6. Can the magnitude of particle’s displacement be greater than the distance traveled? Explain.
Ans: No, the magnitude of the displacement is always less than or equal to the distance travelled. If two displacements in the same direction are added, then the magnitude of their sum will be equal to the distance travelled. Two vectors in any other orientation will give a displacement less than the distance travelled. If you first walk 3 metres east, and then 4 metres south, you will have walked a total distance of 7 metres, but you will only be 5 metres from your starting point.
7. Which of the following are vectors and which are not: force, temperature, the volume of water in a can, the ratings of a TV show, the height of a building, the velocity of a sports car, the age of the Universe?
Ans: Only force and velocity are vectors. None of the other quantities requires a direction to be described.
8. A book is moved once around the perimeter of a tabletop with the dimensions 1.0 m X 2.0 m. If the book ends up at its initial position, what is its displacement? What is the distance travelled?
Ans: The book’s displacement is zero, as it ends up at the point from which it started. The distance travelled is 6.0 metres.
9. Can the magnitude of a vector have a negative value?
Ans: No, the magnitude of a vector is always positive. A minus sign in a vector only indicates direction, not magnitude.
10. Is it possible to add a vector quantity to a scalar quantity? Explain.
Ans: Addition of a vector to a scalar is not defined.