Describing Motion

Terminology To Know

Scalar – Measurement with magnitude but no direction. Magnitude refers to the size of a measurement or the amount you are counting.

Examples: Distance, Time, Speed. 25 seconds.

Vector – Shows both magnitude & direction. Every time you use a map or give directions, you are using vectors.

Examples: Displacement, Position, Velocity, Acceleration. 5km N.

Reference Point – A starting point used to describe the location or the position of an object.

Motion – The process of changing position.

Distance

Distance = Measures the total length of a journey along every twist and turn on the path. It is a scalar quantity, so it has a magnitude but no direction. Standard unit is m or km. There are 1000m in 1 km.

Example: The race covered a distance of 5.62km along the winding banks of a river.

di = Initial or starting distance

df = Final or end distance

∆d =df - di

Position

Position describes an object’s location, as seen by an observer from a particular viewpoint. The observer is usually assumed to be standing still on Earth’s surface. The objects initial starting position is usually taken as the reference point or origin. Position is a vector, so you must state both its magnitude and direction. An arrow over a small “d” indicates a “vector”.

Example: The school is 3.5km south of my house.

Standard Unit: Metre, m.

d

Displacement

Displacement describes how much an object’s position has changed. If the object ends up back where it started like a runner going completely around a racetrack, its displacement is zero, even if it moved a long way. Displacement is a vector.

Displacement = straight line distance from start to finish.

Standard Unit: Metre, m.

Example: Sarah went 25m west on her bike route.

A car leaves home and drives 10 km to the store and then returns home. The car has driven a total distance of 20 km but its final displacement is 0 km.

Using Vector Quantities

When using vector quantities, opposite directions are given opposite signs.

What is the person’s displacement between 0s and 15s?

Adding Vectors – Textbook Page 205

The difference between two positions (vectors) is equal to the sum of the first vector plus the negative of the second vector.

Look at figure 5.4A and B in your textbook so we can go over the example together.

Sample Problem A & B & C – As a class.

Practice Problems 1-8 on page 209 for homework.

Reviewing Concepts

Copy the table below and decide whether each statement is a scalar or a vector.

A. 5m

B. 30m/s [E]

C. 5km [N]

D. 20°C

E. 4000 calories

F. +5.5m

G. 6m left

Reviewing Concepts

Displacement is the change in position and is represented by the equation below. Df can also equal D2, and Di can also equal D1. The displacement formula is used when two objects are going in the same direction, and you are finding the difference between them.

When you are finding the difference between two positions (vectors), you are finding the sum of the second vector plus the negative of the first vector. This would be when one person walks East, and one person walks West, you are looking for the displacement between their positions.

When you are finding the total displacement, you are adding the vectors, but still giving the opposite sign to the opposite vector.

Time

Time describes when an event occurs. Stopwatches or timers are usually reset to zero at the beginning of an experiment, so the initial time, ti, is usually take as zero. Time interval describes the duration of an event. Time is a scalar quantity.

Standard unit is a second, s.

Example: About 30 minutes into the movie (time), Amy went out of the theatre for about 5 minutes (time interval).

ti = Initial or starting time

tf = Final or end time

∆t =tf - ti

The time interval to move from the fire hydrant to the sign is calculated by:

Uniform Motion

Uniform motion is motion in which the object’s displacement is equal for each time interval. Objects rarely have uniform motion, due to frictional forces (The friction force is the force exerted by a surface as an object moves across it or makes an effort to move across it.) acting on the object. We can ignore these small forces for now, and concentrate on the motion of an object.

Example: If a ball moves 10cm in 1 second intervals, we can say it had uniform motion.

Graphing Uniform Motion – Page 212

Sometimes it is useful to graph the information to help you see if it is uniform or not. A graph of uniform motion will look differently than a graph of non-uniform motion. When the line of best fit connects all points, you will have a graph of uniform motion. If the line of best fit does not connect all points, the object’s motion is not quite uniform.

Rules For Graphing Position Time Graphs

• Always have a title• Label the x and y axis at each end.• Name each axis, ie “Time, s”, “Position, cm[right]”•Draw a line of best fit when the data points are plotted. Remember, a line of best fit does not just connect points, it is a line that goes through as many data points as possible. It will be a straight line or a smooth curve, depending on your graph.

Homework: Due for Monday, December 1st.

To practice time intervals, complete activity 5-1B on page 210. I will post answers for this in class.

To practice graphing motion, please complete activity 5-1C on page 213 and answer the questions. Then, please complete the handout on uniform motion.

We will have an in class assignment Tuesday, December 2nd, so it is important you do the assigned homework and readings every night.