Unit 01 Motion with constant velocity. What we asked about

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1 Unit 01 Motion with constant velocity Outline for this unit: Displacement, Velocity: numerically and graphically Mechanics Lecture 1, Slide 1 What we asked about Would like to see more practice problems in class. I found it challenging to distinguish between average speed and average velocity. I am still confused on interpreting the graph and how to calculate average velocity How to draw a velocity graph from a position vs. time graph. The velocity graphs can be quite tricky to understand because I am very accustomed to only dealing with position-time graphs. The last question about average speed and average magnitude of velocity did not make much sense to me - I do not understand how you would get the answer Discussion on magnitude. Just need a refresher on interpreting a velocity graph. I did not understand the magnitude of speed part of the bridge. I found it difficult to answer the question relating her average speed to the magnitude of her average velocity. Not sure how to quantify this based on the graph chosen. Discuss going from position time to velocity time graph. Thank you! I thought this lecture wasn't too difficult but it would be nice to go over another example in class on the intersecting of people while swimming problems. I would like to do a few more examples with velocity compared to average velocity, compared to speed. How to tell which v-t graph corresponds to a tricky x-t graph This is more from lab, but I struggle with distinguishing the different graphs. I know I will end up confusing them. Is there any good way to remember the directions of the slopes for the different graphs? Graphs Mechanics Lecture 1, Slide 2 1

2 Displacement Change in position! Initial position: x o (sometimes x i ) Final position: x f (sometimes no subscript) Δ means final minus initial Displacement: Δx = x f x o Displacement vs Distance Distance is physically how far you traveled. Example: Odometer on a car. Displacement cares about direction you traveled! Δx = x f x o (subtract initial position from final position) 2

3 Question I start my day in my bed and end my day in my bed. How does the distance I traveled compare to the displacement I have underwent? A. Displacement > Distance B. Displacement = Distance C. Displacement < Distance Velocity Average velocity: a measure of how fast and in what direction an object is going. v average,x = x f - x i t f - t i v average,x = Dx Dt 3

4 Speed vs Velocity Speed is physically how fast you are going. Example: Speedometer on a car. Always positive! Velocity speed and direction you traveled! (+ or -) Example 1.1 A runner goes 2km in a straight line in 430 seconds. She stops and catches her breath and returns to her starting point over a period of 460 seconds. What is her average velocity of both of these periods? What is her average velocity for both of these periods combined? Mechanics Lecture 1, Slide 8 4

5 Displacement and Velocity in One Dimension Displacement (rise) Time taken (run) Rise Run = Slope Mechanics Lecture 1, Slide 9 Graphical Analysis Position (x) Slope related to velocity! Time (t) 5

6 Bridge Question 1 The figure shows x vs. t graphs for four objects. What is the correct ranking of the object s velocities, from the most negative to the most positive? A. v i < v ii < v iii < v iv B. v iv < v i < v ii < v iii C. v iii < v i < v iv < v ii D. v iii < v iv < v ii < v i Slower Negative Slower Positive Faster Positive Faster Negative Bridge Question 2 A bacterium swimming at a constant velocity changes to a new constant velocity as shown in the figure. Which velocity vs time plot represents best the motion of the bacterium? 6

7 Bridge Question 2 Explanation Higher Negative Slope Lower Positive Slope Lower Positive Constant Velocity Answer: D! Higher Negative Constant Velocity Bridge Question 3a A student stays at her initial position for a bit of time, then walks slowly in a straight line for a while, then stops to rest awhile and finally runs quickly back to her initial position along a straight line. Which of the following plots best represents the student s trip? 7

8 Bridge Question 3a (What we thought) This is a speed graph, it does not relate to direction. this shows that the student stops, walks, stops, and the quickly runs. this would all be in the positive direction. It must be C because when the girl rest there is a plateau whereas B has a spike. It can't be D because the girl doesn't run back to her initial position. Resting would mean that there would be horizontal line and then when you are moving, you will form a diagonal line and when you return the slope will change because of the change in direction. Which explanation the most sense to you? Talk to a neighbor and discuss your answer! Bridge Question 3a Explanation stays at her initial position for a bit of time stops to rest walks slowly in a straight line runs quickly back to her initial position 8

9 Bridge Question 3a Extension A student stays at her initial position for a bit of time, then walks slowly in a straight line for a while, then stops to rest awhile and finally runs quickly back to her initial position along a straight line. Which of the following plots best represents the student s trip? What is wrong with this graph? A. She starts at x=0 B. First slope is negative, so her velocity is negative C. She Spends her rest at negative position D. She doesn t return back to initial position Bridge Question 3b A student stays at her initial position for a bit of time, then walks slowly in a straight line for a while, then stops to rest awhile and finally runs quickly back to her initial position along a straight line. Which of the following statements is true about the average speed and the magnitude of the average velocity of the student during her trip? A. Her average speed is greater than the magnitude of her average velocity. B. Her average speed is the same as the magnitude of her average velocity. C. Her average speed is less than the magnitude of her average velocity. D. We cannot tell without knowing the farthest point the student went. 9

10 Bridge Question 3b (What we thought) A. Her average speed is greater than the magnitude of her average velocity. Speed is greater because the average velocity is 0 because her final and initial points are the same value. B. Her average speed is the same as the magnitude of her average velocity. her average speed was constant, which it is same as her average velocity. C. Her average speed is less than the magnitude of her average velocity. the change in direction shows that the magnitude is greater D. We cannot tell without knowing the farthest point the student went. Since speed looks at distance over time and average velocity looks at the change in position over time, we would need to know the farthest point she walked in order to calculate her speed and velocity Equation for constant velocity For situation where the velocity is constant, we can rearrange the average velocity equation to: x = x o + vt Initial position = position at time t + velocity multiplied by time 10

11 Quick Problem Solving Ann is racing Beth to a finish line 100 meters away from the start line. Ann can run at a constant velocity of 2.5 m/s and Beth can run at a constant velocity of 1.5 m/s, Beth is allowed to start at the 25 meter mark. Who wins the race? A. Ann B. Beth C. It is a tie Ann 2.5 m/s 1.5 m/s Beth 0m 25m 100m QUESTION The velocity vs. time plot of some object is shown to the right. v(t) = Dx Dt Which diagram below could be the Displacement vs. time plot for the same object? A B C Mechanics Lecture 1, Slide 22 11