Velocity Graphs. RHS Physics. RHS Physics. Review: Position Time Graphs. Slope on a position time graph is velocity. Time (s) Position (m)

Transcription

1 February 7, 214 Velocity Graphs Position (m) Review: Position Time Graphs Slope on a position time graph is velocity. 1

2 Velocity Graphs February 7, 214 Here are graphs of the VELOCITY of 4 people. The PINK person is stationary the entire time. The GREEN double arrow is moving at a constant velocity forward. The RED person starts out at the same velocity as the GREEN, but steadily increases. The BLUE person is moving slowly, but backwards. Slope on Velocity Graphs Slope on a V t graph is ACCELERATION. For Green, Pink and Blue, the slope is zero and there is no change in their velocity. They are on "cruise control" or constant velocity. a= m/s/s. But the Red line velocity is changing. Every second that goes by, the m/s is changing. a > m/s/s. 2

3 Units of Slope on Graphs Velocity February 7, 214 Start with the slope formula. Don't use numbers, just units. Does it look familiar? Pull to reveal the answer. Pull Slope on Velocity Graphs slope is increasing, velocity is changing v is unchanging, cruise control stationary 3

4 Calculus In Arithmetic, there is 4 major functions, adding, subtracting, multiplication and division. In Calculus, there are 2 major functions. Derivatives (finding slope) and Integrals (finding area). We have focused on slope. Let's look at area for a while. February 7, 214 Area under a Constant Velocity Cu Here is a person moving at constant velocity. What does the area under the curve represent? 4

5 February 7, 214 Area under a Constant Velocity Cu Area= (l)(w) =(velocity)(time) =(m/s)(s) =m {these are the units for displacement} Area on a V t graph is displacement. Area=d=(v)(t) {rearrange} v=d/t (this should be familiar from science 1) Area under an accelerating Veloci The RED car starts at the same velocity as the BLUE car, but continually speeds up. It will cover the same distance as the BLUE car, plus more. 5

6 February 7, 214 Create a formula for the total displ v f v i Create a formula for the total displ v f Vf Vi A 2 =1/2(b)(h)=1/2(t)(v f v i ) v i A 1 = (l)(w)=(v i )(t) Some Hints Pull 6

7 Create a Second formula for d T v f v i February 7, 214 The height of the triangle changes with time (see different black lines). Create a Second formula for d T The height of the triangle also changes slope, which is acceleration on a v t graph. 7

8 Create a 2nd formula for d T v f at v i February 7, 214 The height of the triangle has something to do with a & t. Rearrange the Science 1 formula. a= v f v i t at= v f v i Create a formula for the total displ at Repeat the formula creation, but with a new height of the triangle. Pull tab when ready. 8

9 February 7, 214 Create a formula for the total displ A 2 =1/2(b)(h)=1/2(t)(at) A 1 = (l)(w)=(v i )(t) at HINTS. Then, pull tab when ready. Pull Kinematics Formulas We now have many kinematics formulas, mostly from using the area under a v t curve. You will need these memorized so you can do complex problems quickly. V=d/t (constant velocity ONLY) a= v f v i t d=1/2 (v f +v i )t d=v i t +1/2at 2 v f 2=v i 2+2ad 9

10 February 7, 214 Feb 2 3:14 PM 1