Chapter 2 – Motion in one dimension Time and Position PHY 113 C General Physics I 11 AM – 12:15 PM TR Olin 101 Plan for Lecture 2: Chapter 2 – Motion in one dimension Time and Position Time and Velocity Time and Acceleration Special relationships for constant acceleration Problems 1.1,1.6,1.10,1.11 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Some updates/announcements 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Webassign Experiences so far iclicker exercises: Webassign Experiences so far Have not tried it Cannot login Can login Have logged in and have completed one or more example problems. Textbook Experiences Have no textbook (yet) Have complete physical textbook Have electronic version of textbook Textbook is on order Other 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Comment on Webassign #1 problem: 7. A pet lamb grows rapidly, with its mass proportional to the cube of its length. When the lamb's length changes by 16%, its mass increases by 16.8 kg. Find the lamb's mass at the end of this process. Problem solving steps Visualize problem – labeling variables Determine which basic physical principle(s) apply Write down the appropriate equations using the variables defined in step 1. Check whether you have the correct amount of information to solve the problem (same number of knowns and unknowns). Solve the equations. Check whether your answer makes sense (units, order of magnitude, etc.). 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

7. A pet lamb grows rapidly, with its mass proportional to the cube of its length. When the lamb's length changes by 16%, its mass increases by 16.8 kg. Find the lamb's mass at the end of this process. L 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

i>clicker exercise: What did you learn from this problem? It is a bad idea to have a pet lamb This was a very hard question I hope this problem will not be on an exam My physics instructor is VERY mean All of the above. 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Motion in one-dimension 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Graphical representation of position (displacement) x(t) t (s) 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Comment: Your text mentions the notion of a “scalar quantity” in contrast to a “vector quantity” which will be introduced in Chapter 3. In most contexts, a scalar quantity – like one-dimensional distance or displacement can be positive or negative. Another comment: Your text describes the time rate of change of displacement as “velocity” which, in one-dimension is a signed scalar quantity. In general “speed” is the magnitude of velocity – a positive scalar quantity. 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Graphical representation of position (displacement): x(t)  time rate of change of displacement = velocity: v(t) t (s) 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Instantaneous velocity vB vC vA vD vE vF t (s) 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Demonstration of tangent line limit 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Average velocity versus instantaneous velocity 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Average velocity iclicker exercise: This results is: Exact Approximate 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Webassign Example 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Instantaneous velocity using calculus x v 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Anti-derivative relationship x t 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Velocity 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Acceleration 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Rate of acceleration iclicker exercise How many derivatives of position are useful for describing motion: 1 (dx/dt) 2 (d2x/dt2) 3 (dx3/dt3) 4 (dx4/dt4)  8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Anti-derivative relationship 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Examples v(t) x(t) 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Examples v(t) x(t) 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Summary 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Another example x(t) v(t) 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

From webassign: 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Another example (m/s) (s) 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Another example -- continued (m/s) (s) 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Special relationships between t,x,v,a for constant a: 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Special relationships between t,x,v,a for constant a: 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Special case: constant velocity due to earth’s gravity In this case, the “one” dimension is the vertical direction with “up” chosen as positive: a = -g = -9.8 m/s2 y(t) = y0 + v0t – ½ gt2 y0 = 0 v0 = 20 m/s At what time tm will the ball hit the ground ym = -50m ? Solve: ym = y0 + v0tm – ½ gtm2 quadratic equation physical solution: tm = 5.83 s 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2

Helpful mathematical relationships (see Appendix B of your text) 8/29/2013 PHY 113 C Fall 2012 -- Lecture 2