- Distinguish between distance and displacement.
- Distinguish between speed and velocity.
- Define and classify vector and scalar quantities.
- Use scale diagrams, or otherwise, to find the magnitude. and direction of the resultant of a number of displacements or velocities.
- State what is meant by the resultant of a number of forces.
- Carry out calculations to find the rectangular components of a vector.
- Use scale diagrams, or otherwise, to find the magnitude and direction of the resultant of a number of forces.

Aids to Understanding

Distance and Displacement

Where did the (23^{0})come from and why do we need it?
Estimate the distance you might walk on a typical school day and
compare it with your overall displacement.

Speed and Velocity

Look at the diagram of the Moon and Earth. Suppose the moon is above the Earth as shown. Suppose this position is UP. After 15 days the Moon will be below the Earth and suppose this position is DOWN. Calculate the velocity, average speed, distance travelled and displacement of the moon during this 15 day period. Information you may need is readilly available on the internet.

Scalars and Vectors

Impulse is defined as Force x Time and is a vector. However Work done is defined as Force x Displacement and is a scalar. The rule is a vector x vector = scalar but vector x (or divided by) scalar = vector. This also follows from the vector dot product a.b you may have studied in maths. If Pressure = Force/Area, is pressure a vector or Scalar?

Scale Diagrams

Try the following problem. Remember the resultant vector is always drawn at the **centre** of the compass.
Suppose our ship now travels with a bearing 080^{o}
for 6km, the ship changes direction and travels with a bearing 200^{o} for 4 km, the ship again changes
direction and travels a further 10 km on a bearing of 140^{o}. Find the the resultant displacement vector,
ie locate the position of the ship relative to where it started.

Resultant Force

Suppose a 2 kg picture is hanging on the wall. It is not moving so the upwards force due to the two strings is equal to
the weight of the picture. Using a scale diagram, or otherwise, find the force exerted by each string. The force exerted by
a string (or rope or cable) is called the **Tension** in the string.

Rectangular components of a vector

Suppose a person pulls a 50 kg lawn mower with a force of 100 N at an angle of 25^{o}.
Find the horizontal and vertical components
of the force. NOTE: The person is exering an upwards force and a horizontal force on the lawn mower but it
only moves horizontally and not upwards. Why is this?

To help distinguish speed and velocity further consider the following. If a car had an average speed of 20 ms

You are invited to calculate the speed and velocity of the plane after 300 s, if it continues in the same circular route.

Scalar | Vector |
---|---|

Distance | Displacement |

Speed | Velocity |

Mass | Weight (force) |

Time | Acceleration |

Temperature | Impulse |

Click for vector homework suggestion :) Click for solutions