1. One Dimensional Motion Review

2. Motion In One Dimension Simplest type of motion We set the frame of reference – Example, when we set the origin in a coordinate system Can represent motion many ways – Motion diagram – Particle model – Algebraic Equation – Graphs

3. Vocabulary Displacement – change in position – Δx = xf – xi – Can be positive or negative; it's a vector Velocity (avg velocity) - displacement divided by time interval – Slope on position-time graph – V = Δx / Δt – Vector – needs direction

4. Vocabulary, cont. Speed – Absolute value of velocity – Distance traveled over a certain time period – But no direction necessary (scalar quantity) Instantaneous Velocity – velocity at a specific time/location

5. Remember: Velocity can be negative – Just means the displacement was in the negative direction Ex: to the left of the origin on a number line Negative Velocity tells you the direction travelled – Does not mean it moved slower!

6. Acceleration Measures the rate of change in velocity (requires a force) Answers the question: How is speed changing?

7. Cars are sometimes measured by their "0-60" value This is a measure of the car's acceleration ability

8. Acceleration and Speed Positive acceleration and positive speed When displacement and velocity are positive, the final velocity (vf) is greater than the initial velocity (vi) resulting in a positive acceleration.

9. Acceleration and Speed Negative Acceleration and positive speed When slowing down in the positive direction, the acceleration is negative Deceleration

10. Animation

11. Equation for Acceleration

12. Example A Cessna Aircraft goes from 0 m/s to 60 m/s in 13 seconds. Calculate the aircraft's acceleration. 4.62 m/s 2

13. Example The Cessna now decides to land and goes from 60 m/s to 0 m/s in 11 s. Calculate the Cessna's deceleration.

14. More on Acceleration and Speed Constant acceleration is different from constant speed. Motion with zero acceleration appears as a straight horizontal line on a speed versus time graph. zero accelerationconstant speed

15. Constant Acceleration Constant acceleration is sometimes called uniform acceleration. A ball rolling down a straight ramp has constant acceleration. constant acceleration increasing speed

16. Acceleration and Speed constant negative acceleration decreasing speed An object can have acceleration, but no speed. Consider a ball rolling up a ramp. As the ball slows down, eventually its speed becomes zero.

17. Animation Which car or cars is undergoing an acceleration? Which car experiences the greatest acceleration?

18. Animation Question Consider the position- time graph at the right. Each one of the three lines on the position- time graph corresponds to the motion of one of the three cars. Match the appropriate line to the particular color of car.

19. Example A sports car can accelerate at a rate of 2.5 m/s/s. How long will it take to reach a speed of 50 m/s? Knowns: a = 2.5 m/s 2 vi = 0 m/s vf = 50 m/s Unknown: t = ? Equation: a = (vf – vi)/ t Rearranged Equation: t = (vf – vi)/ a Plug and Chug: (50 m/s – 0 m/s) / 2.5 m/s 2 t = 20 sec

20. Example When dropped, most objects accelerate at 10 m/s/s. If an acorn falls from an oak tree and takes 1.3 seconds to hit the ground, how fast will it be going just before it strikes? Known: a = -10 m/s 2 t = 1.3 s vi = 0 m/s Unknown: vf= ? Equation: Equation: a = (vf – vi)/ t Rearranged Equation: vf = vi + at Plug and Chug: 0 m/s + (-10m/s 2 * 1.3 sec) vf = -13 m/s

21. Graphing Slope of displacement graph is velocity Slope of velocity graph is acceleration

22. Acceleration and Slope Acceleration is the change in speed over the change in time. The slope of the speed versus time graph is the acceleration.

23. Reading a VT Graph What is the acceleration from t=0s to t=3s? What is the acceleration from t=3 s to t=5s? What is the acceleration from t=8s to t=9s?