1. PH 201 Dr. Cecilia Vogel Lecture 2

2. REVIEW  Motion in 1-D  velocity and speed  acceleration  velocity and acceleration from graphs  Motion in 1-D  position  displacement  average velocity  Special case:  Constant velocity OUTLINE

3. Average Velocity  Average velocity is displacement divided by time interval  Average velocity always has the same direction as displacement

4. Average Velocity on a Graph  On a graph of position vs. time, average velocity is the slope of a line connecting two points on the graph. x t xixi xfxf titi tftf

5. Velocity x t Average velocity, given by slope of straight line, doesn’t describe everything that happens during the time interval. (Instantaneous) velocity describes what happens at a given instant – at a single point on the graph.

6. Instantaneous Velocity x t If you take a smaller time interval, you more accurately reflect what’s happening at that instant.

7. Velocity on Graph  On a graph of position vs. time, (instantaneous) velocity is the slope of a line tangent to the curve at that instant. x t positive negative zero 0123-2-3

8. Summary  Positive velocity  Moving forward  Value of position, x, increasing  Slope of x vs. t is positive  Negative velocity  Moving backward  Value of position, x, decreasing  Slope of x vs. t is negative  Zero velocity  Stopped (maybe just for an instant)  Occurs any time motion changes direction  x vs. t graph is horizontal (maybe just for an instant)

9. Instantaneous Speed  Instantaneous speed is just the magnitude of the instantaneous velocity.  Always positive.

10. Average Speed  Average speed is the distance traveled divided by the time interval.  Compare to  Average velocity is displacement divided by time interval  Small wording difference, big difference in results: Ex: Object goes 5 cm in the negative direction in one second. v ave =-5 cm/s, s ave =+5 cm/s Ex: Object goes 5 cm in the negative direction then two cm in the positive direction, all in one second. v ave =-3 cm/s, s ave =+7 cm/s

11. Ave Speed Example  Example  Sharrona drives to her friend’s house along a straight road at a constant 35 mph. She forgot something, so returns home, traveling only 25 mph.  Find her average velocity and average speed.  Problem-solving hints.

12. Instantaneous Speed  Instantaneous speed is just the magnitude of the instantaneous velocity.  Always positive.  Note it is also the limit as  t approaches zero of the average speed.  As time interval goes to zero, there’s no time to change direction, so speed = |v|

13. Acceleration  Average acceleration is  Change in velocity over the time interval  Object’s acceleration is positive if  v f > v i  velocity is increasing  Remember that from -50 to -40 is an increase  Speed NOT necessarily increasing!!

14. Direction of Acceleration  Three ways to find acceleration direction  Is velocity (not speed!) increasing?  if so, accel is +  don’t forget -10 > -50  What direction do you feel tossed when you accelerate that way?  imagine a car  acceleration is OPPOSITE that  What way would you have to push/pull to cause that acceleration?  acceleration is in that direction

15. Examples Way #1  Velocity positive, speed increasing ex: v i = +30 mph, v f = +60 mph velocity is increasing, a is __+___  Velocity positive, speed decreasing ex: v i = +30 mph, v f = +20 mph velocity is decreasing, a is __-___

16. Way #1, cont’d  Velocity negative, speed increasing ex: v i = -30 mph, v f = -60 mph velocity is decreasing, so a is _-__ (speeding up, but negative accel!!!)  Velocity negative, speed decreasing ex: v i = -30 mph, v f = -20 mph velocity is __creasing, so a is __

17. Way #2  Your body is an accelerometer, you feel pushed opposite the acceleration.  Velocity positive, speeding up feel pushed back opposite that, a is back or -  Velocity positive, slowing down feel pushed _____ opposite that, a is ____

18. Way #2 cont’d  Velocity negative, speeding up feel pushed forward opposite that, a is back or -  Velocity negative, slowing down feel pushed ___ opposite that, a is ___

19. Sign of Acceleration  Acceleration requires a force. How would you have to push something to change its velocity?  Object’s velocity is positive, if you want it to speed up  must push forward,  Push forward -> a is forward or +  Object’s velocity is positive, if you want it to slow down  must push backward,  push back -> a is ___

20. Sign of Acceleration  Object’s velocity is negative, if you want it to slow down  push forward,  so a is forward or +  Object’s velocity is negative, if you want it to speed up  push backward,  so a is ___