Car Lab: Results. Were you able to plot: Position versus Time? Velocity versus Time? Copyright 2010 Pearson Education, Inc.

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Norah Jefferson
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1 Car Lab: Results Were you able to plot: Position versus Time? Velocity versus Time?

3 Chapter 2.2: Acceleration

4 Acceleration Acceleration is the rate at which velocity changes with time. Average acceleration: Acceleration is a vector. It can be positive or negative, indicating direction. SI units are m/s 2. Acceleration occurs when there is a change in speed or direction.

5 Acceleration Acceleration is the rate of change of velocity.

6 Acceleration Increasing speed and decreasing speed (deceleration) should not be confused with the directions of velocity and acceleration: Note the sign of the acceleration by itself does not indicate if an object speeds up or slows down.

7 Deceleration There is a difference between negative acceleration and deceleration: Negative acceleration is acceleration in the negative direction as defined by the coordinate system. Deceleration occurs when the acceleration is opposite in direction to the velocity.

8 Sensing Acceleration The human body cannot detect velocity. Flying on a plane at 560 mph seems much like sitting still. The human body is great at detecting acceleration. When you speed up or slow down in a car, you are pushed back or pushed forward. What about other instruments? Can they sense velocity and/or acceleration? Estimate velocity from position or Doppler effect

9 Example 1 An advertisement says a car can go from 0 to 26.8 m/s (i.e. 60 mph) in 6.2 s. What is the average acceleration on the car? a = (26.8 m/s) / (6.2 s) = = 4.3 m/s 2 A drag racer deploys a parachute and slows down from 130 m/s to 45 m/s in 3.0 s. What is the acceleration? a = (45 130)/3.0 = = -28 m/s 2

10 Acceleration can be determined graphically. The slope of a velocity vs. time line is the acceleration. Constant slope means constant acceleration.

11 The instantaneous acceleration is the average acceleration in the limit as the time interval becomes infinitesimally short.

12 Example A subway train speeds up with a constant acceleration of 1.2 m/s 2. How much time does it take for the train s speed to increase by 4.1 m/s? a = v/ t 1.2 = 4.1/ t t = (4.1 m/s)/(1.2 m/s 2 ) = = 3.4 s

13 Question 2.14a v versus t graphs I a) decreases Consider the line labeled A in b) increases the v vs. t plot. How does the c) stays constant speed change with time for d) increases, then decreases line A? e) decreases, then increases v A t B

14 Question 2.14a v versus t graphs I a) decreases Consider the line labeled A in the v vs. t plot. How does the speed change with time for line A? b) increases c) stays constant d) increases, then decreases e) decreases, then increases v A B t In case A, the initial velocity is positive and the magnitude of the velocity continues to increase with time.

15 Question 2.14b v versus t graphs II a) decreases Consider the line labeled B in b) increases the v vs. t plot. How does the c) stays constant speed change with time for d) increases, then decreases line B? e) decreases, then increases v A t B

16 Question 2.14b v versus t graphs II Consider the line labeled B in the v vs. t plot. How does the speed change with time for line B? a) decreases b) increases c) stays constant d) increases, then decreases e) decreases, then increases v A B t In case B, the initial velocity is positive but the magnitude of the velocity decreases toward zero. After this, the magnitude increases again, but becomes negative, indicating that the object has changed direction.

17 Equation of Motion with Constant Acceleration

18 Equation of Motion with Constant Acceleration Definition of acceleration: a = (v f v i )/(t f t i ) Rearrange: v f = v i + a (t f t i ) Defining t i =0, velocity at any time: v f = v i + a t

19 Example An eagle has an initial velocity of 5.0 m/s and an acceleration of 1.3 m/s 2. What is the velocity of the eagle at t=2.0 s? v = v i + a t v = (1.3) 2.0 = 7.6 m/s

20 Constant Acceleration v i v f

21 Constant Acceleration

22 Equation of Motion for Constant Acceleration

23 Sets of Equations (t i = 0, t t f )

24 Example

25 Stopping and Take-off Distance

26 Example

27 Position-Time Graphs for Constant Acceleration

28 Constant Velocity

29 Constant Acceleration

30 Constant Acceleration

31 Constant Acceleration

32 Example

33 Stopping Distance Is this plot correct?

34 2-car Example

35 Graphical Analysis of Motion

36 Sets of Equations (t i = 0, t t f )

37 Galileo Ramp Lab

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