Kinematics Motion in 1-Dimension

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1 Kinematics Motion in 1-Dimension Lana Sheridan De Anza College Jan 16, 2018

2 Last time unit conversions (non-si units) order of magnitude calculations how to solve problems

3 Overview 1-D kinematics quantities of motion

4 Kinematics in 1-dimension We begin by studying motion along a single line. This will encompass situations like cars traveling along straight roads objects falling straight down under gravity

5 Vectors and Scalars scalar A scalar quantity indicates an amount. It is represented by a real number. (Assuming it is a physical quantity.)

6 Vectors and Scalars scalar A scalar quantity indicates an amount. It is represented by a real number. (Assuming it is a physical quantity.) vector A vector quantity indicates both an amount (magnitude) and a direction. It is represented by a real number for each possible direction, or a real number and (an) angle(s).

7 Notation for Vectors In the lecture notes vector variables are represented using bold variables. Example: k is a scalar x is a vector In the textbook and in writing, vectors are often represented with an over-arrow: x The magnitude of a vector, x is written: x = x

8 Examples of Scalars and Vectors Some physical quantities that are scalars are temperature mass pressure Some physical quantities that are vectors are velocity force

9 Distance vs Displacement How far are two points from one another? Distance is the length of a path that connects the two points. Displacement is the length together with the direction of a straight line that connects the starting position to the final position. Displacement is a vector.

10 Position Quantities position displacement distance x x = x f x i d Position and displacement are vector quantities. Position and displacement can be positive or negative numbers. Distance is a scalar. It is always a positive number.

11 Position Quantities position displacement distance x x = x f x i d Position and displacement are vector quantities. Position and displacement can be positive or negative numbers. Distance is a scalar. It is always a positive number.

12 Position Quantities position displacement distance x x = x f x i d Position and displacement are vector quantities. Position and displacement can be positive or negative numbers. Distance is a scalar. It is always a positive number. Units: meters, m

13 Position t (s) x (m) Such a plot is called a position time graph. Notice the alternative representations o motion of the car. Figure 2.1a is a pictor The starting30 position of 0the cargraphical is x i = 30 representation. m i, the finaltable position 2.1 is is a tabu x f = 50 m i Using an alternative representation is oft the situation in a given problem. The u The distance the car travels is d = 50 m 30 m = 20 m Position, Displacement, Distance Example The car moves to the right between positions and. x (m) x The displacement of the car is x = x f x i = 20 m i. x (m)

14 Position, Displacement, Distance Example The starting position of the car is x i = 30 m i, the final position is x f = 60 m i. The distance the car travels is d = 130 m. The car moves to the right between positions and. x (m) x x (m) The displacement of the car is a The car moves to the left between x positions = x f and x i. = ( 60i) 30i m = 90 m i x b

15 Speed We need a measure how fast objects move. speed = distance time If an object goes 100 m in 1 second, its speed is 100 m/s.

16 Speed Speed can change with time. For example, driving. Sometimes you are on the highway going fast, sometimes you wait at a stoplight. Instantaneous speed is an object s speed at any given moment in time.

17 Speed Speed can change with time. For example, driving. Sometimes you are on the highway going fast, sometimes you wait at a stoplight. Instantaneous speed is an object s speed at any given moment in time. Average speed is the average of the object s speed over a period of time: average speed = total distance traveled time interval

18 Velocity Driving East at 65 mph is not the same as driving West at 65 mph.

19 Velocity Driving East at 65 mph is not the same as driving West at 65 mph. There is a quantity that combines the speed and the direction of motion. This is the velocity.

20 Velocity Driving East at 65 mph is not the same as driving West at 65 mph. There is a quantity that combines the speed and the direction of motion. This is the velocity. Velocity is a vector quantity. Speed is a scalar quantity.

21 Velocity Driving East at 65 mph is not the same as driving West at 65 mph. There is a quantity that combines the speed and the direction of motion. This is the velocity. Velocity is a vector quantity. Speed is a scalar quantity. If a car drives in a circle, without speeding up or slowing down, is its speed constant?

22 Velocity Driving East at 65 mph is not the same as driving West at 65 mph. There is a quantity that combines the speed and the direction of motion. This is the velocity. Velocity is a vector quantity. Speed is a scalar quantity. If a car drives in a circle, without speeding up or slowing down, is its speed constant? Is its velocity constant?

23 Velocity How position changes with time. Quantities velocity average velocity instantaneous speed average speed v v avg = x t v or v d t

24 Velocity How position changes with time. Quantities velocity average velocity instantaneous speed average speed v v avg = x t v or v d t Can velocity be negative?

25 Velocity How position changes with time. Quantities velocity average velocity instantaneous speed average speed v v avg = x t v or v d t Can velocity be negative? Can speed be negative?

26 Velocity How position changes with time. Quantities velocity average velocity instantaneous speed average speed v v avg = x t v or v d t Can velocity be negative? Can speed be negative? Units: meters per second, m/s

27 point. A graphical representation of thi 0 30 Such a plot is called a position time graph Notice the alternative representations o The displacement 20 of the38car is motion x = 20of mthe i. car. Figure 2.1a is a pictor 30 0 The distance the car travels is d graphical = 20 m. representation. Table 2.1 is a tabu Using an alternative representation is oft The time for 50 the car to 253 move this the far situation is 10 seconds. in a given problem. The u What is the average velocity of the car? What is the average speed of the car? Average Velocity vs Average Speed Example The car moves to the right between positions and. x (m) x (m) x

28 point. A graphical representation of thi 0 30 Such a plot is called a position time graph Notice the alternative representations o The displacement 20 of the38car is motion x = 20of mthe i. car. Figure 2.1a is a pictor 30 0 The distance the car travels is d graphical = 20 m. representation. Table 2.1 is a tabu Using an alternative representation is oft The time for 50 the car to 253 move this the far situation is 10 seconds. in a given problem. The u What is the average velocity of the car? What is the average speed of the car? Average Velocity vs Average Speed Example The car moves to the right between positions and. x (m) average velocity v avg = x t = 2 m/s i (same in this case) x (m) average speed = d t = 2 m/s x

29 Average Velocity vs Average Speed Example The displacement of the car is 90 m i. The distance the car travels is d = 130 m. The time for the car to move A F is 50 seconds. Average velocity? Average speed? the situation in a given problem. The u The car moves to the right between positions and. x (m) x x (m) x The car moves to the left between positions and a b

30 Average Velocity vs Average Speed Example The displacement of the car is 90 m i. The distance the car travels is d = 130 m. The time for the car to move A F is 50 seconds. Average velocity? Average speed? the situation in a given problem. The u The car moves to the right between positions and. x (m) x x (m) x average velocity v avg = x average speed = d t a The car moves to the left between t positions and. = 2.6 m/s = 1.8 m/s i Not the same! b

31 Question Quick Quiz Under which of the following conditions is the magnitude of the average velocity of a particle moving in one dimension smaller than the average speed over some time interval? A A particle moves in the +x direction without reversing. B A particle moves in the x direction without reversing. C A particle moves in the +x direction and then reverses the direction of its motion. D There are no conditions for which this is true. 1 Serway & Jewett, page 24.

32 Question Quick Quiz Under which of the following conditions is the magnitude of the average velocity of a particle moving in one dimension smaller than the average speed over some time interval? A A particle moves in the +x direction without reversing. B A particle moves in the x direction without reversing. C A particle moves in the +x direction and then reverses the direction of its motion. D There are no conditions for which this is true. 1 Serway & Jewett, page 24.

33 Conceptual Question y rankings, remember that zero is greater than a negative value. If two values are equal, show that they are equal in your ranking.) c Conceptual Questions 1. denotes answer available in Student So 1. If the average velocity of an object is zero in some time interval, what can you say about the displacement of the object for that interval? 2. Try the following experiment away from traffic where you can do it safely. With the car you are driving moving slowly on a straight, level road, shift the transmission into neutral and let the car coast. At the moment the car comes to a complete stop, step hard on the brake and notice what you feel. Now repeat the same experiment on a fairly gentle, uphill slope. Explain the difference in what a person riding in the car feels in the two cases. (Brian Popp suggested the idea for this 1 Serway & Jewett, page Y g w a w e 7. ( b i z 8. ( b

34 Acceleration Speed and velocity can change with time. Acceleration is the rate of change of velocity with time. acceleration = change in velocity time interval

35 Acceleration Speed and velocity can change with time. Acceleration is the rate of change of velocity with time. acceleration = change in velocity time interval If an object is moving with constant speed in a circular path, is it accelerating?

36 Acceleration Quantities acceleration average acceleration a a avg = v t Acceleration is also a vector quantity.

37 Acceleration Quantities acceleration average acceleration a a avg = v t Acceleration is also a vector quantity. If the acceleration vector is pointed in the same direction as the velocity vector (ie. both are positive or both negative), the particle s speed is increasing.

38 Acceleration Quantities acceleration average acceleration a a avg = v t Acceleration is also a vector quantity. If the acceleration vector is pointed in the same direction as the velocity vector (ie. both are positive or both negative), the particle s speed is increasing. If the acceleration vector is pointed in the opposite direction as the velocity vector (ie. one is positive the other is negative), the particle s speed is decreasing. (It is decelerating.)

39 Summary quantities of motion Homework Walker Physics: Ch 2, onward from page 47. Conc. Ques: 1, 3, 9, 13; Probs: 1, 3, 5, 7, 9, 13, 35

Kinematics Motion in 1-Dimension

Kinematics Motion in 1-Dimension Lana Sheridan De Anza College Jan 15, 219 Last time how to solve problems 1-D kinematics Overview 1-D kinematics quantities of motion graphs of kinematic quantities vs