Velocity Versus Time Graph - Understanding Uniform Motion

1. Quiz Quiz: • You have 10 minutes • I will give you a 30 second warning • Please be sure to include identification!

2. Outline Position versus Time • Graphing position versus time • Uniform Motion 3125 2761 Mdcl1 Mdcl!

3. QQ13: simultaneity Quick Quiz:

4. Answer QQ13 The d-t graph 300 John x [m] Monica 0 150 100 0 t [s]

5. Solution:

6. Outline Velocity versus Time • Quiz • Instantaneous Velocity • Getting Velocity from the Position Graph

7. Instantaneous Velocity • Velocity is the rate of change in position • Average velocity is averaged over some time interval • If that time interval gets smaller and smaller, the average velocity starts to better represent the velocity at a particular point in time • Once the time interval gets small enough that the velocity appears to be constant over that time interval, the average velocity is the same as an instantaneous velocity

8. Displacement : Average velocity: x x2 x x1 t t1 t2 t • Instantaneous velocity is the average over an ‘infinitesimal’ time interval :

9. When the time interval is large relative to thecurvature of the x vs. t graph, the average velocityover that interval does not necessarily accurately represent the range of instantaneous velocities during that interval. x2 x1 t2 t1

10. As we shrink the time interval, the average velocity over that interval approaches the instantaneous velocity in the middle of the interval: x2 x1 t2 t1

11. As we shrink the time interval, the average velocity over that interval approaches the instantaneous velocity in the middle of the interval: x2 x1 t2 t1

12. As we shrink the time interval, the average velocity over that interval approaches the instantaneous velocity in the middle of the interval: x2 x1 t2 t1

13. x t • Instantaneous velocity at a point on the position versus time graph is given by the derivative of the path at that point • A derivative is the rate of change, it is the tangent slope to a graph at a point • That means that the slope of the tangent at that point is the instantaneous velocity

14. Ex. Finding Velocity Finding velocity from a potion versus time graph The slope at each point of the position versus time graph is the velocity at each point of the velocity versus time graph

15. Example Solution Demo: Passport motion sensor using data studio with x and v graphs shown simultaneously

16. Do for next class: • Read: sections 2.5, 2.6 • Suggested problems: 2.3, 2.5