Applied Science 10

Describing Motion: Velocity

Where Am I? If you want to give accurate information about an object's location, you must tell where it is compared to some reference point. For example, if you want your friends to find you quickly and easily in the mall, you might say, "Meet me just outside the music store at 7:30 PM." In this example, you are the object and the music store is the reference point. Here's another example: your ATV breaks down in the woods but you have your cellphone with you and are able to tell your parents you are about 15 km East past a bridge along a certain trail. In this example, the bridge is the reference point and the ATV is the object.

Frame of Reference A person walking along a wet beach leaves a string of footprints. The trail of footprints in the sand shows where the person was moving and so is called the frame of reference. The reference point in this example would be the spot place where the person started their walk along the sand. A car moving along a snowy road leaves tire tracks. The lines of tire tracks show where the car was moving and so is called the frame of reference. The spot where the car began its motion along the road is its reference point. When an object is moving we may not always be able to see its tracks (we could not see the tracks of a skateboard along pavement) but it is always moving in its frame of reference and it always will have some starting point called the reference point.

Scalars and Vectors A Phys Ed class creates treasure maps. One map says "stand just inside the football field by the entrance next to the baseball diamond and then walk 50 paces" Another map says "stand just inside the football field by the entrance to the playing field next to the baseball diamond and then walk 50 paces to the left along the edge of the field". Which map is more useful? The one that gives distance and direction. To say, "walk 50 paces" is giving a value called a scalar - it is just the distance. The other map that gave both the distance and direction to walk is giving a type of value called a vector.

Position and Displacement Position and displacement are two closely related ideas and we can describe them at the same time. If you are 10 steps to the left of a drinking fountain, your position is easy to state: it is just "10 steps to the left of the drinking fountain". If you stand still, your position is the same and of course, if you move, your position changes. For example, what is your position if you move 5 more steps to the left? Are both motions in the same direction? Yes, both to the left. So, it's simple; just add the 5 steps to the 10 steps. Now your new position is 15 steps left of the drinking fountain. What about your displacement? You moved 5 steps to the left so your displacement is just "5 steps to the left".

Here's another example. What if you were 20 steps to the left of the drinking fountain and you moved 7 steps to the right? Are both motions in the same direction? No, your first steps were to the left but your last steps were to the right. Its still simple but subtract the 7 steps from the 20 steps. Now your new position is 13 steps to the left of the drinking fountain. What is your displacement? You moved 7 steps to the right and so your displacement is "7 steps to the right".

FYI: Remember the example of walking along the wet beach? Each footstep is called a time-position value because the person makes each footprint at an exact time and each footprint is at an exact position along the beach. Do you ever look up a jet aircraft moving soundlessly across the sky? (I always wonder where they're going. A vacation in Florida? On a business trip to Europe? Single or a couple or a family?) Each puff of white in the jet's exhaust trail (called its contrail) is a time-position value, just like each step in the wet sand.

Average Velocity An object's average velocity tells us how far it moves in what time. Use the following equation: v_AVG = d / t. The distance should be in meters and the time should be in seconds. For example, if an elephant took nine minutes to walk 250 m across a patch of grassland, its average velocity is just 250 m / 540 s = 0.46 m/s.

Time-Position Graphs

Graphs are a very useful, sometimes instant way of understanding. Just looking at a time-position graph gives a good idea of the speed and direction of an object. Note: calculating the slope gives a more accurate idea about the object's speed.

No motion A time-position graph for "no motion"

is a flat line intersecting the y-axis at the spot where

the object was resting. The slope = 0 in this example.

How could you demonstrate this? Just stand still.

Constant velocity The time-position graph for constant (uniform) velocity is a straight, sloping line intersecting the y axis at the spot where the object started its motion. The slope of the line indicates how fast the object was moving. How could you demonstrate constant velocity? Just walk at an even pace.

FYI: we already know to find an object's speed with the equation: v = d/ t. Now look at this: to find the slope of a time-position graph, we use the same equation. So, when we find the slope of a time-position graph, we are really finding the speed of the object! For a time-distance graph, slope = speed!

Time-Velocity Graphs

Although we can find an object's velocity from the slope of a time-position graph, a more direct way is to look at a time-velocity graph.

No motion The plot is a flat line right on the

x axis itself because the speed = 0 there.

Uniform velocity The plot is a

flat line intersecting the y axis at

the object's proper velocity value.

FYI: we already know the area of a rectangle is: a = b * h. The distance an object travels is: d = v * t. If we draw a rectangle between the plot line and the x axis in a time-velocity graph, we can find its area with a = b * h (or h * b). But, in a time-velocity graph, the h is the velocity and the b is the time and so when we are doing the h * b to find area, we are really doing the v * t to find distance. So, for a time-velocity graph, area of rectangle = distance object travels.