Quiz

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Quiz:

Position versus Time

3125

2761

Mdcl1

Mdcl!

Outline

• Graphing position versus time• Uniform Motion

QQ13: simultaneity Quick Quiz:

Answer QQ13

The d-t graph

x [m]

t [s]

300

01500 100

John

Monica

Solution:

Velocity versus Time

Outline

• Quiz• Instantaneous Velocity• Getting Velocity from the Position Graph

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

Average velocity :

txvx /

tt1 t2 t

x

xx1

x2

12 xxx Displacement :

• Instantaneous velocity is the average over an ‘infinitesimal’ time interval :

xvdtdx

txt

0

t1 t2

x1

x2

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.

t1 t2

x1

x2

As we shrink the time interval, the average velocity over that interval approaches the instantaneous velocity in the middle of the interval:

t1 t2

x1

x2

As we shrink the time interval, the average velocity over that interval approaches the instantaneous velocity in the middle of the interval:

t1 t2

x1

x2

As we shrink the time interval, the average velocity over that interval approaches the instantaneous velocity in the middle of the interval:

• 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

t

x

slopedtdxvx

0100200300400500600700

0 1 2 3 4 5 6 7 8 9 10

t [s]

x[m

]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

Example Solution

0100200300400500600700

0 1 2 3 4 5 6 7 8 9 10

t [s]

x[m

]

-150

-100

-50

0

50

100

150

200

0 2 4 6 8 10

t [s]

v[m

/s]

Demo: Passport motion sensor using data studio with x and v graphs shown simultaneously

Do for next class:• Read: sections 2.5, 2.6

• Suggested problems: 2.3, 2.5