Non-Uniform Motion and Acceleration

Topics covered today Introducing Acceleration Types of Acceleration Positive Acceleration Negative Acceleration Interpreting Graphs with Acceleration Position-Time Graph (PT Graph) Velocity-Time Graph (VT Graph)

Introducing Acceleration Previously, we learned that velocity is defined as the change in displacement of an object over a period of time. Well, acceleration is defined as the change in speed of an object over a period of time. Remember that acceleration is always a vector quantity. acceleration

Formulas for Acceleration We worked with the formula Now, we’re learning a new formula v = velocity d = displacement t = time a = acceleration v = velocity t = time

Types of Acceleration Essentially, there are two different types of acceleration: - Positive Acceleration: where the direction of acceleration is THE SAME as the direction of motion, so the object speeds up. - Negative Acceleration: where the direction of acceleration is the OPPOSITE OF the direction of motion, so the object slows down.

Example Problems A shuttle craft accelerates from rest to a velocity of 50 m/s [upward] in 4.00 s. What is it’s acceleration? Tanya slams on the breaks of her friend’s quad and slows down from 20 m/s [E] to 5 m/s [E] in 6.00 seconds. What is her acceleration?

Example #1 Answers

Example #2 Answers

Example Problems Continued Example #3 Homer Simpson is driving the infamous Oscar Meyer Weinermobile down the Springfield Freeway. If he is moving with an initial velocity of 32 m/s and he accelerates at a rate of 0.6 m/s 2 until he is driving at a velocity of 41 m/s, how long was he accelerating for? Example #4 Cody was driving a 2007 Aston Martin DB9 at 108 km/h. They decide to test out this car's maximum acceleration so they put the "petal to the metal" for 8 seconds. If the car's final speed after 8 seconds of acceleration was 252 km/h, at what rate was the car accelerating at (in m/s 2 )?

Example #3 Answer Homer Simpson is driving the infamous Oscar Meyer Weinermobile down the Springfield Freeway. If he is moving with an initial velocity of 32 m/s and he accelerates at a rate of 0.6 m/s 2 until he is driving at a velocity of 41 m/s, how long was he accelerating for?

Example #4 Answers Example #4 Cody was driving a 2007 Aston Martin DB9 at 108 km/h. They decide to test out this car's maximum acceleration so they put the "petal to the metal" for 8 seconds. If the car's final speed after 8 seconds of acceleration was 252 km/h, at what rate was the car accelerating at (in m/s 2 )?

Types of Acceleration Here are the four types of acceleration

Rearranging the formula Solve for: Time Final velocity

Practice Example 1:Lightening McQueen is racing Doc around the dirt track by Radiator Springs. They both start at rest and accelerate at 26.0 m/s 2 in 5.00 sec. What velocity do they reach before the first corner?

Practice Example 2:The Flash starts from rest and accelerates to 32.0 m/s 2 to chase after a villain. How long does it take him, if his final velocity is 27.0 m/s ?

Independent Practice Questions found in Notes They’re also textbook questions, so have a look through the back to check your answers.

Using Graphs to Analyze Motion Often, graphs are used in physics to describe the motion of an object in ways that are more clearly understandable then either word problems or formulas. Today we are looking at two new types of graphs that are very similar to DT and ST: Displacement-Time Graphs (PT) Velocity-Time Graphs (VT)

Position-time graphs Two ways to show acceleration graphically: Positive acceleration Negative acceleration Slope is ___________ dd tt

Position-Time Graphs What was the line of best fit like in all the position-time graphs that we have been creating? In accelerated motion, the line of best fit is a smooth curve A Position-Time (PT) Graph is very similar to a DT graph except that we now record the displacement of the object on the y-axis, not distance.

Displacement-Time Graphs Displacement-Time or PT Graphs are used to record or measure the changes in position an object undergoes: Since, a change in position involves a direction, you need to pick a direction to treat as positive. Here are the parts of the graph you need to know: The X-axis is the time The Y-axis is the displacement [direction] The Slope of the line is the average velocity

Differences between DT and PT graphs The only significant difference between DT and PT graphs is that you now need to consider the direction of motion of the object. Motion in the opposite direction that you chose to be “positive” is negative. The Slope of the line is now the average velocity, which also has a direction.

Interpreting Graphs with Acceleration On a PT or DT Graph X-axis is the time Y-axis is the displacement (or distance) Slope of the line was the velocity (or speed) On a VT or ST Graph X-axis is the time Y-axis is the velocity (or speed) Slope of the line was the acceleration Area under the graph is the displacement (distance)

Using the Slope to Find Information

Interpreting a Graph Now, displacement MUST include a direction because this graph is recording how far AND in what direction you are moving in respect to where you started. So, what would: 1) A displacement of 15 m [N] mean? 2) A displacement of -5 m [N] mean?

Creating and Interpreting a PT Graph The data to the left was collected for an object in motion. Draw a PT Graph for this motion Determine the slope of the line. What value does this slope represent? Time t (s) Position [N] d (m)

Interpreting PT Graphs

Velocity-time graphs Change in velocity over time How do we calculate slope? Line of best fit will be straight, either increasing or decreasing Positive acceleration Negative acceleration v v tt

Velocity-Time Graphs Velocity-Time or VT Graphs are used to record or measure the changes in velocity an object undergoes: Here are the parts of the graph you need to know: The X-axis is the time elapsed. The Y-axis is the velocity traveled in a direction. The Slope of the line is the object’s acceleration in that direction. The Area under the graph is the total displacement traveled by the object in that time interval.

Reading a typical VT Graph

Creating and Interpreting a VT Graph The data to the left was collected on a street racer. Draw a VT Graph for this motion Determine the slopes of this graph. What value does this slope represent? What is the final displacement? Time t (s) Velocity of a street racer v [East] (m/s)

What are the slopes of this graph and what do they represent? Interpreting VT Graphs

What is the total displacement of the racer between 0 – 4 seconds? What is the total displacement of the racer between 4 – 6 seconds? Interpreting VT Graphs

What is the displacement of the racer between 8 – 14 seconds? What is the total displacement traveled by the racer before stopping? Interpreting VT Graphs

Physics Assignment B1.2: Check and Reflect (p145) Questions 6, 7, and 8 These are all graphing problems and will take some time to complete! When you are done that, start reading B.1.3 Acceleration

Interpreting Position – Time Graphs

Interpreting Velocity – Time Graphs

Understanding Patterns of Graphs

Independent Practice B1.3: Check and Reflect (p154) Questions 5, 6, 7, 9 and 10.