Constant Acceleration
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1 Constant Acceleration Ch. in your text book Objectives Students will be able to: ) Write the definition of acceleration, either in words or as an equation ) Create an equation for the movement of an object based on a velocity vs. time graph ) Use the general velocity equation to solve a problem ) Create an a vs. t graph based on a v vs. t graph
2 Review: Based on the graph, what is the object s velocity at second? At seconds? Velocity vs. Time Graphs
3 Based on the graph, what is the object s velocity at second? At seconds? Velocity does not have to be constant. Velocity vs. Time Graphs
4 Acceleration Acceleration a change in velocity over time The equation looks like this: a Unit for acceleration is m/s Changing velocity means you are: speeding up slowing down changing direction
5 Velocity vs. Time Graphs v(m/s) Based on the graph, what is the average acceleration for this person? What is the slope of the graph? What does the slope of a velocity vs. time graph represent?
6 Acceleration Acceleration is a vector, which means it has a direction. While it can be positive or negative, that doesn t necessarily indicate that you are speeding up or slowing down. Speeding up means your speed is going away from 0. Slowing down means your speed is getting closer to 0.
7 Acceleration Check for understanding Both graphs have a negative slope. Which one shows a car slowing down?
8 Acceleration Check for understanding Both graphs have a positive slope. Which one shows a car slowing down?
9 Acceleration In this class, we will use the terms positively accelerating or negatively accelerating. The term decelerating can be deceptive. Check for understanding ) What does a positive slope mean on a velocity graph? ) What does a negative slope mean on a velocity graph? ) What does a flat line mean on a velocity graph? ) What would a steep slope mean compared to a shallow slope?
10 Velocity vs. Time Graphs Check for understanding Based on the graph, describe, in words, the motion of this person.
11 Getting Acceleration From Velocity Graphs Based on the graph, what is the acceleration for this person? a a a The slope on the velocity graph is the acceleration.
12 Acceleration vs. Time Graphs Acceleration =. m/s They are going. m/s for seconds a (m/s )
13 Acceleration vs. Time Graphs a (m/s )
14 Acceleration vs. Time Graphs a (m/s ) 0 - -
15 Tangent Lines We made acceleration graphs from velocity graphs. Now it s time to make velocity graphs from position graphs (again) but for an object that is accelerating. For that, we need to first understand tangent lines. Tangent a straight line that touches a curve at a point, but if extended, does not cross the curve at that point The line is tangent to the circle at the red dot.
16 Tangent Lines Here are some bad examples. Please do not ever draw these.
17 Here are some good examples. Tangent Lines
18 Acceleration Graphs From Position Graphs x (m) This is a position graph for an object that is accelerating. What does the velocity vs. time graph look like?. Draw tangent lines at three points. The beginning, end, and middle usually work out best.
19 Acceleration Graphs From Position Graphs x (m) This is a position graph for an object that is accelerating. What does the velocity vs. time graph look like?. Determine the velocity (slope) at each point. Your only choices are positive, negative, or zero. Zero Positive More positive
20 Acceleration Graphs From Position Graphs. Place a point on the velocity graph for each of the points on the position graph where you drew a tangent line. Draw a line connecting the dots. x (m) More positive Positive Zero
21 Acceleration Graphs From Position Graphs. Draw the acceleration graph. x (m) a (m/s )
22 Acceleration Graphs From Position Graphs Try this one on your own. x (m) a (m/s )
23 To Finish Up On your white boards, answer the following questions: ) Determine the velocity of an object based on a position vs. time graph (be sure to check the scale on the vertical axis) ) Create an equation of an object based on a position vs. time graph ) Use the general position equation to solve a problem ) Create a velocity vs. time graph based on a position vs. time graph x (m) 0 0
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