SNC2D – Physics M. M. Couturier Position-Time Graphs SNC2D – Physics M. M. Couturier

Position-Time Graphs As the term suggests, a position-time graph is a graph where position is plotted on the y-axis and time is plotted on the x-axis.

Position-Time Graphs Since velocity is related to position and time (m/s), the slope of the function will reveal the average velocity.

Position-Time Graphs However, to understand the nature of the velocity, we must understand all four kinds of slopes: increasing, decreasing, zero and infinite.

Position-Time Graphs This is an example of a zero slope. The displacement here is ∆d = 0 over a period of time, t. The average velocity here is therefore: Vavg = ∆d = 0 = 0 ∆t t Essentially, the object is at rest.

Position-Time Graphs This is an example of an increasing slope. ∆d and ∆t are both positive and therefore, Vavg will also be positive. Also, since it is a straight line (linear), the velocity is constant, meaning the velocity is the same.

Position-Time Graphs This is an example of a decreasing slope. ∆d is negative and since ∆t can only be positive, Vavg will be negative. They are either driving towards a reference point or returning to their origin.

Position-Time Graphs There is another possibility, but it leaves the realm of Newtonian physics; that of the infinite slope, where we have a ∆d but with a t = 0. This essentially means that an object has gone from one place to another in 0 time. We will not study this situation further.

Position-Time Graphs In order to calculate the average velocity using a position-time graph, you need to isolate two points on a single line. Look at the position-time graph below and write down the coordinates of any two points on the line.

Position-Time Graphs Since the average velocity is defined by: Vavg = ∆d ∆t The two points that we have selected provide both ∆d and ∆t.

Position-Time Graphs Lets say that you selected (t,d) as (5,50) and (0,0). Your ∆d = (50-0) and your ∆t = (5-0), hence; Vavg = ∆d = (50 – 0) = 50 ∆t (5-0) 5 Vavg = 10 m/s Does it matter which point you choose?

Position-Time Graphs Lets say that you selected (t,d) as (4,40) and (3,30). Your ∆d = (40-30) and your ∆t = (4-3), hence; Vavg = ∆d = (40 – 30) = 10 ∆t (4-3) 1 Vavg = 10 m/s It does not matter.

Position-Time Graphs Never hesitate to draw on the graph that is provided to you in the following manner.

Position-Time Graphs Okay; lets describe qualitatively what is happening in each of these situations.

Position-Time Graphs Possible solution for practice A: An object begins to move away from its initial position at an increasingly faster rate. (Very scientific) Possible solution for practice A: Brittany was originally walking away from a dog, faster at every step, but then realize the dog was angry so she picked up the pace. Later she realized that she was running away. (More realistic)

Position-Time Graphs Does that make sense?

Position-Time Graphs Possible solution for practice B: A distant object is being pulled towards another a point, at an increasingly faster rate. (Very scientific) Possible solution for practice B: Chris, far from home, gets into a cold car. At first it travels very slowly, but over time it warms up and therefore its velocity increases over time. (More realistic)

Position-Time Graphs Does that make sense?

Position-Time Graphs Another way we can look at motion is to use ticker tapes. Imagine a car with an oil leak! If it leaks a drop of oil every second, we can establish relatively how fast the car is going?

Position-Time Graphs In your opinion, which car is going faster?

Position-Time Graphs In your opinion, which car is going faster? The first line: the displacement is greatest. You will notice that the displacements are all the same, so the velocity of the car is constant.

Position-Time Graphs In your opinion, which car is going faster? The second line: the displacements are small but increasing. The car is increasing its velocity over time. Hence the car is accelerating.

Position-Time Graphs In your opinion, which car is going faster? The third line: the displacements are very small at first but become very large. The car was probably at rest and then accelerated to a large velocity in a short period of time.

Position-Time Graphs Task 1: Look at the graph below and determine the vaverage in each case and then write a short story to explain the events. Be creative.

Position-Time Graphs Task 2: Look at the graph below and determine the vaverage in each case and then write a short story to explain the events. Be creative.

Position-Time Graphs Lets do a test: http://dev.physicslab.org/Document.aspx?doctype=3&filename=Kinematics_PositionTimeGraphs.xml