The Physics of Motion

Physics is a science that has a mathematical basis. Our first area of study in Physics is the motion of objects. Motion is described by words such as position, displacement, velocity, acceleration, distance and speed. These terms that are used can be divided into two categories. The quantity is either a vector or a scalar. These two categories can be distinguished from one another by their definitions:

• Scalars are quantities that are described by a magnitude alone.
• Vectors are quantities that are described by both a magnitude and a direction.

This is similar to numbers and integers in mathematics. Numbers show magnitude (size) only; the number 5 indicates size only. Integers show both magnitude (size) and direction (+ or – means above or below zero); the integer +5 means 5 above or to the right of zero.

Classify the following as either scalar or vector quantities:

5 m, north 25ºC 40mL 23m/s, South

The physicist uses specific language to describe objects in motion. In order to understand motion we must know the meaning of these words.

Position gives the location (distance and direction) of the object as seen from an observer’s viewpoint. The distance and direction are given relative to a reference point. Example the car is 5m, south of the flagpole. Position is a vector quantity; position states magnitude and direction.

Direction can be stated in a number of different ways; in Science 10 linear motion uses: “+” to indicate up or right and “–“ to indicate down or left. For motion on a plane (a surface) we indicate direction of motion using radial rotation from a starting position; North is 0º, East is 90º, South is 180º and West is 270º.

Displacement is a vector quantity that refers to the object's change in position. Displacement is the straight-line distance between two points. Displacement does not take the path followed into account; displacement is concerned with the start position and the end position; that is the change in position. Displacement is calculated as: final position – initial position (finds the change in position).

In the following example the person walking around the block. She walks 3m north (A to B) then 4m east (B to C). To calculate the displacement we must add the vectors together. To add vectors we complete the parallelogram and the resultant vector is the diagonal. In this example the hypotenuse (AC) shows that she is 5m 53º from where she started. The change in position (displacement) is 5m 53º.

Distance is a scalar quantity that refers total length of a journey. Distance takes the length of the path followed. Distance is concerned with how you get from where you started to where you finish. In the example she walked a total of 7m (3m + 4m) to get from A to B to C.

What are the total displacement and the total distance if she walks A to B to C to D and back to A?

Total Displacement equals 0. Why?

Total Distance equals 14m. Why?

What is the distance and displacement of the skier in her travel from A to B to C to D?

(Remember vectors for linear motion have two components: sign to show direction and magnitude to show position relative to a starting position.)

Velocity is a vector quantity that describes the rate at which an object changes its position. Because velocity is a vector quantity the direction must be indicated, the velocity of an object must keep track of direction. The direction of the velocity vector is the same as the direction that an object is moving. It is not enough to say that an object has a velocity of 50 km/hr. You must include direction information in order to fully describe the velocity of the object, 50 km/hr, at 0º (north).

Speed is a scalar quantity that refers to how fast an object is covering a distance (moving). A fast-moving object (high speed) covers a large distance in a small amount of time, a slow-moving object (low speed) take a long time to cover a short distance. Speed does not keep track of direction. This is one of the essential differences between speed and velocity.

As an object moves, it usually undergoes changes in speed. For example, during a trip to school, there are many changes in speed. Rather than the speedometer maintaining a steady reading, the needle constantly moves up and down to reflect the stopping and starting and the accelerating and decelerating. One instant, the car may be moving at 50 km/hr and another instant, it might be stopped (i.e., 0 km/hr). Yet during the course of the trip to school the person might average 30 km/hr.

Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity. An object not changing its velocity is not accelerating. Anytime an object's velocity is changing, that object is said to be accelerating.

How can an object change velocity?

1. Velocity can increase (object speeds up).

2. Velocity can decrease (object slows down)

Velocity is a vector quantity so a change in direction will change the velocity

3. If the object changes direction to move up or to the right there is + change in velocity.

4. If the object changes direction to move down or to the left there is – change in velocity.

Acceleration occurs when there is a change in velocity.

Time is the scalar measure used to describe when an event occurs. Example: The show starts at 7:00pm. Time interval describes the duration of an event. Example: The show starts at 7:00pm and ends at 9:00pm, the show lasts for 2 hours. The time interval can be calculated as the difference in times (final – initial) 9:00pm – 7:00pm = 2 hr.

The difference or change in is described by delta (Δ) that is calculated as the final value minus the initial value (Δ = final – initial).

Displacement = position_final – position_initial ( Δ= _final – _initial)

Time interval (Δt = t_f – t_i )

Moving object often change speed or velocity during motion, you need to distinguish between average speed (or velocity) and instantaneous speed ( or velocity). The difference is as follows.

Instantaneous Speed - speed at any given instant in time.

Instantaneous Velocity - velocity at any given instant in time.

Example: Looking at the speedometer and noting your speed at a moment in time. A police officer using a radar gun notes your instantaneous speed. Remember velocity is the same as speed except there is a direction included.

Average Speed the average of all speeds during a time interval; average speed is calculated by a distance/time ratio.

Average Velocity the average of all velocities during a time interval; average velocity is calculated by a displacement/time ratio.

Example: If Truro is 100km from Dartmouth and it takes 1 hour for you to travel to Truro from Dartmouth, you travel at an average speed of 100km/hr. You speed during the trip will vary but on the overall trip you traveled at an average of 100km/hr.

The instantaneous speed is the speed that the speedometer reads at any given instant in time. The average speed is the average of all the speedometer readings during the course of the trip.

Velocity is the same as speed except a direction must be included.