LEARNING OBJECTIVES

Knowledge & Understanding

- Distinguish between scalar and vector quantities and give examples.
- Add and subtract vectors by calculation.
- Multiply vectors by numbers and scalars.
- Resolve a vector into two components at right angles to each other.
- Represent vector quantities graphically as directed line segments.
- Use vectors to solve problems, including relative motion.
- Express relationships between objects in motion relative to each other.
- Distinguish between extrapolation and interpolation.
- Determine formula from graphical information.

Scientific Techniques

- Draw graphs to illustrate the relationships between physical quantities in the form:

- y =k.x y=k.x
^{2}y=k.x^{3}y=k.1/x y=k.(x) - Plot a graph from experimental data and interpret graphs.
- Use graphical means to analyse a set of experimental data and determine the relationship between the quantities involved.
- Add and subtract vectors by scale drawing.

COMPLEX REASONING PROCESSES

- Add and subtract vectors at angles other than right angles.
- Calculate relative velocity as applied to aeroplanes, boats in water currents and similar relative motion.

- Scalar quantities have magnitude only. They can be added, subtracted, multiplied and divided by normal arithmetic.
- Vector quantities have direction as well as magnitude. They must be added or subtracted by the head to tail rule.
- The resultant of vectors at right angles to each other can be calculated using Pythagoras' Theorem or the sin, cos and tan trigonometric functions; for vectors at other angles the cos rule or sin rule may be more useful.
- Change in a measurement (D) = final measurement - initial measurement.
- Vectors can be resolved into two components at right angles to each other.
- Motion is always relative to some other frame of reference.
- The velocity of A relative to B is written as v
_{AB}. - The velocity of A to C is the vector sum of the velocity of A to B and the velocity of B
to C and can be written as: v
_{AC}= v_{AB}+ v_{BC} - The velocity of A to B is the opposite of the velocity of B to A: hence v
_{AB}= - v_{BA} - The forward motion of an object is not slowed or speeded up by air or water currents at right angles to the motion.
- Graphs have two axes. The x-axis or the horizontal axis is for the independent variable or cause. The effect of that cause is plotted on the y-axis and is called the dependent variable.
- Points on a graph should be plotted as a dot within a circle or as a cross.
- The line of best fit for a graph should pass through as many points as possible but for the points that are off the line - there should be an equal amount above the line as below it.
- Points a long way for the line are called spurious or outliers.
- Extending and reading a graph beyond the last plotted point is called extrapolation. Inferring a reading between plotted points is called interpolation.
- The slope or gradient of the line is defined as change in y divided by change in x. For curves, the slope of the tangent is calculated.
- Common terms associated with graphs are: direct proportion (which includes linear and parabolic relationships) and indirect proportion (which includes inversely proportional and other hyperbolic relationships).
- Graphs of the following relationships have characteristic shapes which have been
detailed in this chapter: y µ x, y = mx, y = mx + c, y µ x², y µ x³, y µ
1/x, y µ x
^{½} - Relationships between variables can be proven by plotting the predicted function of x on the x-axis and examining to see whether the graph is a straight line.
- Computer spreadsheets have a graph, chart or plot function which enables you to look for characteristic graph shapes.