Uniform motion, slope and speed Position-time graphs Uniform motion, slope and speed

Review What is distance? What is it measured in? What is displacement? What must you include when giving the measurement of displacement? What is the formula for displacement? What is time? What is time measured in? What is time interval? What is the formula for time interval? What directions are positive? What directions are negative?

Uniform motion Q: What do you think uniform motion is? A: Objects moving in uniform motion travel equal displacements in equal time intervals Basically, if a ball was rolling in uniform motion, it would not speed up, slow down or change directions – it would just keep on going

Motion diagrams

Motion diagrams Motion diagrams shows the object’s position at different times throughout the movement You can use this data to plot a graph, which can be used to analyze motion

Position-time graphs POSITION-TIME GRAPH When you plot the TIME data on the X-AXIS and the POSITION data on the Y-AXIS, you create a POSITION-TIME GRAPH Time (s) Position (m) 1 15 2 30 3 45 4 60 5 75 6 90 7 105 8 120

Graph Reminders The x-axis is located at the bottom of the graph (horizontal axis) THIS IS WHERE THE TIME GOES The y-axis is located along the left side of the graph (vertical axis) THIS IS WHERE THE POSITION GOES

Best-Fit line In uniform motion, the plots on a graph will line up in a straight line. In the real world, however, we rarely see uniform motion, so the plots on a graph may not line up It is useful to use a best-fit line that passes through as many of the points as possible A best-fit line is a smooth curve or straight line that most closely fits the general shape outlined by the points

Best-fit line The slope on a position-time graph shows the AVERAGE movement over time

Slope The slope is the best-fit line drawn on the graph that represents which direction an object is travelling in The slope of a line can be either Horizontal (zero) Slanting up (positive) Slanting down (negative)

Slope Finding a graph’s slope is simple: Slope = rise (sound familiar?) run The rise = position; the run = the time Position is measured in (m) and time is measured in (s)  therefore slope is measured in m/s

Positive slope A positive slope represents an object that is moving in a positive direction (East, Right, North or Up) A positive slope is represented as a line that slants UP TO THE RIGHT Example: flying from Vancouver to Toronto. Each second you move further East across Canada

Zero slope Zero slope represents an object that is NOT moving Zero slope is a straight, HORIZONTAL line, meaning that the object is not being displaced during that period of time Example: You are biking to school and you come to a stop at an intersection. At the intersection, you are not moving

Negative slope A negative slope represents an object that is moving in a negative direction (West, Left, South or Down) A negative slope is represented by a line that slants DOWN TO THE RIGHT Example: Putting a golf ball west towards the hole. As time goes on, the ball rolls closer West towards the hole.

Velocity Velocity is the change in displacement of an object divided by the time interval Velocity describes both the speed and the direction of motion Velocity is represented as: v Velocity is measured in: meters per second (m/s) and includes the direction of travel

Velocity Speed = how fast Velocity = how fast in what direction Example: the speed limit is 100 km/h Velocity = how fast in what direction Example: the escalator moves you upwards at 1m/s You can find velocity with this formula:

Reminders Displacement just means how much an object’s position changes from the origin (where it started) It can be found with this formula: Δd = df – di Time interval just means how long it takes for an event to occur It can be found with this formula: Δt = tf – ti So, since velocity is just the change in displacement over the change in time v = Δd / Δt

Think about it… Velocity is an object’s change in position over a change in time A position-time graph shows an object’s change in position over a period of time Therefore, the slope on a P-T graph represents an object’s velocity The rise = position; the run = the time Slope = or Slope = --------- df - di   tf – ti