Physics 1201W Lecture 2 Wednesday, September 10
Chapter 1: 1-D Motion Displacements can occur in two and three dimensions – we’ll concentrate on 1-D for now
Displacement
Position vs. Time
Average vs. Instantaneous Velocity Instantaneous velocity, v: slope of tangent to x vs. t graph at a given instant
Average vs. Instantaneous Velocity Instantaneous velocity, v: slope of tangent to x vs. t graph at a given instant
Derivatives A menu of derivatives will be provided on quizzes and final Don’t forget slope of tangent: Etc.
Speed Speed is greater than or equal to zero Definitions for speed: – Instantaneous speed = absolute value (“magnitude”) of instantaneous velocity – Average speed = total distance (not displacement) traveled divided by time elapsed, the time required to travel the total distance – It is typically not useful to use the absolute value of the average velocity! Velocity characterized by magnitude and direction; speed characterized solely by magnitude.
Formulae Infinitesimal displacement: Average velocity: Displacement: Instantaneous velocity: Average speed: Instantaneous speed:
Speed Example #1 It normally takes you 10 min to travel 5.0 mi to school along a straight road. You leave home 15 min before class begins. Delays caused by a broken traffic light slow down traffic to 20 mi/h for the first 2.0 mi of the trip. If you drive at your usual speed (the one that allows you to get to school in 10 min) for the remaining 3.0 mi, will you be late for class?
Speed Example #1 – Solution Pt. 1
Speed Example – Solution Pt. 1
Speed Example #1 – Solution Pt. 2
Speed Example #1: Graph
Speed Example #2 Two cars are traveling along a straight road. Car A maintains a constant speed of 80 km/h and car B maintains a constant speed of 110 km/h. At t = 0, car B is 45 km behind car A. (a) How much farther will car A travel before car B overtakes it? (b) How much ahead of A will B be 30 s after it overtakes A?
Speed Example #2 – Solution Pt. 1
Speed Example #2 – Solution Pt. 2
Speed Example #2 – Solution Pt. 3
Speed Example #2: Graph
Instantaneous Velocity vs. Time