2. Motion in One DimensionSection 2 What do you think? Which of the following cars is accelerating? –A car shortly after a stoplight turns green –A car approaching a red light –A car with the cruise control set at 80 km/h –A car turning a curve at a constant speed Based on your answers, what is your definition of acceleration?

3. Motion in One DimensionSection 2 Preview Objectives Changes in Velocity Motion with Constant Acceleration Sample Problem Chapter 2 Section 2 Acceleration

4. Motion in One DimensionSection 2 Objectives Describe motion in terms of changing velocity. Compare graphical representations of accelerated and nonaccelerated motions. Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration.

5. Motion in One DimensionSection 2 Acceleration Acceleration is the rate at which velocity changes over time. What are the units? –SI Units: (m/s)/s or m/s 2 –Other Units: (km/h)/s or (mi/h)/s An object accelerates if its speed, direction, or both change. Acceleration has direction and magnitude. Thus, acceleration is a vector quantity Acceleration = 0 implies a constant velocity (or rest)

6. Motion in One DimensionSection 2 Classroom Practice Problem Find the acceleration of an amusement park ride that falls from rest to a velocity of 28 m/s downward in 3.0 s. –Answer: 9.3 m/s 2 downward

7. Motion in One DimensionSection 2 Velocity and Acceleration

8. Motion in One DimensionSection 2 Direction of Acceleration Describe the motion of an object with v i and a as shown to the left. Moving right as it speeds up Moving right as it slows down Moving left as it speeds up Moving left as it slows down ViVi a ++ +- -- -+

9. Motion in One DimensionSection 2 Graphing Velocity The slope (rise/run) of a velocity/time graph is the acceleration. –Rise is change in v –Run is change in t This graph shows a constant acceleration. Average speed is the midpoint.

10. Motion in One DimensionSection 2 Graph of v vs. t for a train Describe the motion at points A, B, and C. Answers –A: accelerating (increasing velocity/slope) to the right –B: constant velocity to the right –C: negative acceleration (decreasing velocity/slope) and still moving to the right

11. Motion in One DimensionSection 2 Chapter 2 Motion with Constant Acceleration When velocity changes by the same amount during each time interval, acceleration is constant. The relationships between displacement, time, velocity, and constant acceleration are expressed by the equations shown on the next slide. These equations apply to any object moving with constant acceleration. These equations use the following symbols:  x = displacement v i = initial velocity v f = final velocity  t = time interval Section 2 Acceleration

12. Motion in One DimensionSection 2 Useful Equations 1. 2. 3. 4. 5.

13. Motion in One DimensionSection 2 Chapter 2 Equations for Constantly Accelerated Straight-Line Motion Section 2 Acceleration

14. Motion in One DimensionSection 2 Classroom Practice Problems A bicyclist accelerates from 5.0 m/s to 16 m/s in 8.0 s. Assuming uniform acceleration, what distance does the bicyclist travel during this time interval? –Answer: 84 m An aircraft has a landing speed of 83.9 m/s. The landing area of an aircraft carrier is 195 m long. What is the minimum uniform acceleration required for safe landing? –Answer: -18.0 m/s 2

15. Motion in One DimensionSection 2 Sample Problem Final Velocity After Any Displacement A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500 m/s 2. What is the velocity of the stroller after it has traveled 4.75 m?

16. Motion in One DimensionSection 2 Sample Problem, continued 1. Define Given: v i = 0 m/s a = 0.500 m/s 2  x = 4.75 m Unknown: v f = ? Diagram: Choose a coordinate system. The most convenient one has an origin at the initial location of the stroller, as shown above. The positive direction is to the right. Chapter 2 Section 2 Acceleration

17. Motion in One DimensionSection 2 Chapter 2 Sample Problem, continued 2. Plan Choose an equation or situation: Because the initial velocity, acceleration, and displacement are known, the final velocity can be found using the following equation: Rearrange the equation to isolate the unknown: Take the square root of both sides to isolate v f. Section 2 Acceleration

18. Motion in One DimensionSection 2 Sample Problem, continued Tip: Think about the physical situation to determine whether to keep the positive or negative answer from the square root. In this case, the stroller starts from rest and ends with a speed of 2.18 m/s. An object that is speeding up and has a positive acceleration must have a positive velocity. So, the final velocity must be positive. 3. Calculate Substitute the values into the equation and solve: 4. Evaluate The stroller’s velocity after accelerating for 4.75 m is 2.18 m/s to the right.

19. Motion in One DimensionSection 2 Now what do you think? Which of the following cars is accelerating? –A car shortly after a stoplight turns green –A car approaching a red light –A car with the cruise control set at 80 km/h –A car turning a curve at a constant speed Based on your answers, what is the definition of acceleration? How is acceleration calculated? What are the SI units for acceleration?

20. Motion in One DimensionSection 2 Velocity vs. Time Graphs Constant speed

21. Motion in One DimensionSection 2 Velocity vs. Time Graphs + Acceleration

22. Motion in One DimensionSection 2 Velocity vs. Time Graphs Deceleration or negative acceleration

23. Motion in One DimensionSection 2 Velocity vs. Time Graphs Yellow line represents faster acceleration

24. Motion in One DimensionSection 2 Velocity vs. Time Graphs Constant speed of 30 m/s

25. Motion in One DimensionSection 2 Velocity vs. Time Graphs Red line represents faster rate of deceleration (3 m/s 2 ).

26. Motion in One DimensionSection 2 Velocity vs. Time Graphs Red line represents faster acceleration than green, blue line represents deceleration or negative acceleration.