Velocity: Speed with direction! Science 10

Uniform Motion Predicting the behaviour of moving objects can be very complex. Measuring and analyzing motion in the real world is a challenge, so scientists try to simplify their task. Scientists try to model the behaviour of objects that move in almost straight lines at almost constant speed as uniform motion because this can be easily analyzed. Uniform motion: motion at constant velocity, with no change in speed or direction.

Velocity Velocity is a vector quantity which refers to "the rate at which an object changes its position." V = d__ t

Describing the direction of velocity (v) The direction of the velocity vector is simply the same as the direction which an object is moving. If the object is moving rightwards, then its velocity is described as being rightwards. If an object is moving downwards, then its velocity is described as being downwards. Example: So an airplane moving towards the west with a speed of 300 km/hr has a velocity of 300 km/hr, west. Note that speed has no direction (it is a scalar) and velocity is simply the speed with a direction.

Physics teacher walking in circles again… The physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. Determine the average speed and the average velocity. The physics teacher walked a distance of 12 meters in 24 seconds; thus, her average speed was 0.50 m/s. However, since her displacement is 0 meters, her average velocity is 0 m/s. Remember that the displacement refers to the change in position and the velocity is based upon this position change. In this case of the teacher's motion, there is a position change of 0 meters and thus an average velocity of 0 m/s.

Velocity: position (Δdisplacement) vs Velocity: position (Δdisplacement) vs. time graphs Consider a car moving with a constant, rightward (+) velocity of +10 m/s. If the position-time data for such a car were graphed, then the resulting graph would look like the graph at the right. Note that a motion described as a constant, positive velocity results in a line of constant and positive slope when plotted as a position-time graph. This is uniform motion!!!

The slope of a position-time graph is the velocity!!!!!

Calculating average velocity from a position-time graph: Examine the graph at the right which illustrates the motion of a car. Each section of the graph has a different slope representing individual velocities at that stage of the journey. They can easily be calculated by finding individual slopes of that section of the graph. The average velocity of the total graph or trip is found by using the beginning and end points.

Distance Time Graphs The slope of a distance time graph will tell us the Velocity of the object. There are 3 possible cases:

1. Horizontal Line Slope of this line is zero. The speed is zero. If your speed is zero you are NOT MOVING.

2. Uphill Line Slope of this line is POSITIVE. If your speed is positive you are MOVING FORWARD.

3. Downhill Line Slope of this line is NEGATIVE. If your speed is negative you are MOVING BACKWARD.

Try These 1. The car is stopped. 2. The speed of the car is decreasing. 3. The car is coming back.

What is happening here?

What is happening here?

So, if the slope of the position-time graph gives us velocity, and that the graph shows us uniform motion, then… There are only three possible shapes for the graphs to take. No motion, object is stationary d 3. Uniform motion to the left (backward) t d 2. Uniform motion to the right (forward) t

Pause & reflect: Sketch a position-time graph of each object listed below. Describe its slope as positive or negative, and as constant, increasing, or decreasing. A) a stone at rest B) a jogger moving steadily to the right C) a bicycle moving to the left and slowing down D) a rocket moving up at an increasing speed E) a stone falling freely with increasing speed F) a parachutist drifting down at a steady speed