Chapter 3: Vectors

Question 1

Vector quantity

Answer 1

• A quantity with both magnitude and direction
• E.g. displacement - the distance, in a given direction, that an object is located from a defined position
• Vectors can be shown in two ways:
  1. Symbolic
  2. Diagrammatic - an arrow pointing in a specific direction, with its scale length measuring magnitude

Question 2

Speed

Answer 2

• Rate at which a body changes its position, or the distance it travels in a unit of time
• No direction, therefore scalar

Question 3

Velocity

Answer 3

• rate at which a body changes its position in a certain direction, or the displacement of the body in a unit of time
• direction, therefore vector

Question 4

Force

Answer 4

• a push or pull acting on a point or object

- S.I. units of force are Newtons (N)

Question 5

Addition of vectors rules

Answer 5

1. The addition of the vector a to the vector b, will always result in a third vector c.
2. The order of the operation is not important, so a + b = b + a.
3. To add: the head of one vector, a, must be placed so that it touches the tail of the other vector, b. The resultant, c, goes from the tail of the first vector to the head of the last vector.

Question 6

Methods for adding vectors

Answer 6

1. By using scale diagrams
2. By using trigonometric relationships
3. By resolving the vectors into two perpendicular directions

Question 7

Scale diagrams

Answer 7

• define a suitable scale
• establish directions eg. Top of page as North
• construct vectors and determine resultant

Question 8

Trigonometric relationships

Answer 8

• two vectors added gives resultant - usually a triangle

- concept map

Question 9

Subtraction of vectors rules

Answer 9

1. The subtraction of one vector, b, from another, a, will result in a third vector, c.
2. The order of the subtraction is important and it does matter which vector is subtracted from which: a - b = -(b - a).
3. Subtracting b from a can be carried out by using the negative of vector b. This can be done by adding a to -b. All subtraction of vectors can be reduced to addition of vectors: a - b = a + (-b)

Question 10

Scalar quantity

Answer 10

• A quantity which has magnitude (or size), but no direction
• The magnitude is made up of a number and usually an appropriate unit
• E.g. Distance