Distance vs. TimeDistance vs. Time

Analysis of a Distance vs. Time Analysis of a Distance vs. Time GraphGraph

Determining the motion on a Determining the motion on a D vs. T GraphD vs. T Graph

Where did the object start?Where did the object start?

Which direction did it go?Which direction did it go?

Where did the object stop?Where did the object stop?

Is the motion uniform (constant)?Is the motion uniform (constant)?

Is the motion non-uniform (changing)?Is the motion non-uniform (changing)?

Can you tell which is faster? (if 2 or Can you tell which is faster? (if 2 or more objects are present)more objects are present)

d(m)

t(s)

A

Object A is stationary at some positive position from the origin.

d(m)

t(s)

B

Object B moves Object B moves away from origin away from origin with a constant with a constant positive velocity.positive velocity.

d(m)

t(s)

C

Object C start at some positive position and moves away from the origin at a constant positive velocity.

d(m)

t(s)

D

Object D moves away from the origin at a constant positive velocity (slower than previous examples).

d(m)

t(s)

E

Object E start at some positive position and walks toward the origin with a constant velocity.

Distance vs. Time Graphs with Non-Uniform Motion

Changing velocity

(increasing)

Changing velocity (decreasing)

Slope of a D vs. T Graph Slope of a D vs. T Graph

Rise/runRise/run

On a distance vs. time graphOn a distance vs. time graph

–Rise = dRise = df f – d– di i == ΔΔd d

–Run = tRun = tf f – t– tii = = ΔΔt t

Slope = Slope = ΔΔd / d / ΔΔt =…t =…

Average Velocity (VAverage Velocity (Vaveave) )

Using slope to predict motionUsing slope to predict motionOn a On a distance vs. timedistance vs. time graph graph– If slope is 0, then velocity is 0.If slope is 0, then velocity is 0.– If slope is positive, velocity is If slope is positive, velocity is

constant in positive direction.constant in positive direction.– If slope is negative, velocity is If slope is negative, velocity is

constant in the opposite direction.constant in the opposite direction.– If slope is changing, velocity is If slope is changing, velocity is

changing.(i.e. you are changing.(i.e. you are accelerating)accelerating)

d(m)

t(s)

A

B

D

C

Slower than B or C.

Same velocity as

B. V=0

Constant +V

East

High St.

West

EA

B

D

C

Finding position

Vavg = Δd / Δt

Vavg = (df –di)/Δt

df = di + Vavg Δt

(df = final position)

Time to Practice

• Physics Book:– Pg. 85 (2 & 3)– Pg. 87 (5 & 8)– Pg. 89 (9 – 12a)