Distance is the space between two points, commonly measured in metres (m). Distances between two points can depend on the path taken. Time (t) is the duration of an event. Time is often referred to as a time interval and given the symbol  t. A period (T ) is the time interval between two repeating events, such as a pendulum swinging. It is related to frequency as: Graphs are used to illustrate the mathematical relationships of two quantities. Distance and Time 12.1 VOCABULARY time interval slope

By relating time and distance, we can determine speed, which is the distance an object travels (  d) divided by the time interval (  t). The average speed of an object is the total distance the object travelled divided by the total time taken. Instantaneous speed is the speed of an object at a particular instant in time. For example, a car speedometer reads instantaneous speed. For an object travelling at a constant speed (i.e. uniform motion), the average speed is equal to its instantaneous speed. Speed 12.2 VOCABULARY speed average speed instantaneous speed

A distance–time graph has distance on the y-axis and time on the x-axis. The slope of a line on a distance– time graph is equal to average speed. The units for the slope would be metres/second (m/s), the same as speed. Graphing Distance and Time 12.3

We can calculate the instantaneous speed of an object at a particular time by calculating the slope of the tangent to the line of the distance–time graph of the object’s motion. Just as we can use distance and time data to construct a graph, we can derive information about distance, time, and speed from a graph. Graphing Distance and Time 12.3

Distance and displacement are similar, but not identical concepts in science. Distance is a scalar quantity (magnitude only). Displacement is a vector quantity (magnitude and direction) The displacement of an object is its change in position in relation to a point of reference. Displacement and Velocity 12.4 VOCABULARY scalar quantity displacement vector quantity velocity uniform motion

Speed and velocity are also similar, but not identical concepts. Speed is a scalar quantity (magnitude only). Velocity is a vector quantity (magnitude and direction). Velocity is the rate of change of displacement and is given by the equation: The slope of the line of a position– time graph is equal to the velocity of the object. Displacement and Velocity 12.4 VOCABULARY scalar quantity displacement vector quantity velocity uniform motion

Displacement, Time, and Velocity The motion of an object can be described by displacement, time, and velocity. Distance and displacement are similar but not identical concepts in science. Speed and velocity are also similar but not identical concepts. 12 CHAPTER

Displacement, Time, and Velocity Distance–time graphs and position– time graphs can visually display information about an object’s motion. The slope of the line is equal to the speed or velocity of the object. If the slope of the line is changing, the speed or velocity is not constant. If the slope the line is constant, the object is travelling at constant speed or velocity. 12 CHAPTER

Displacement, Time, and Velocity Quantities can be either scalar or vector. Scalar quantities only have magnitude, which is a number with a unit. Vector quantities have both a magnitude and a direction. An object’s speed and velocity can be described in different ways. For example, average speed or velocity, instantaneous speed, and uniform motion (constant speed or velocity). 12 CHAPTER

Displacement, Time, and Velocity Activity With a partner, use a mind map to brainstorm different methods of measuring distance (including length and height of objects). For example, you could measure using a ruler, using the length of your arm, etc. Could all of your distance measuring methods be converted to have the same measurement units, such as metres? If you wanted to measure the distance from school to your home, which method would you use? Explain. For more information on distance, read page 341 in the textbook. 12 CHAPTER

Displacement, Time, and Velocity 12 Key Ideas The motion of an object can be described by displacement, time, and velocity. Distance–time graphs and displacement–time graphs can visually display information about an object’s motion. Quantities can be either scalar or vector. An object’s speed and velocity can be described in different ways. CHAPTER