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Motion Graphs
(d vs t)

 

B. Interpreting Motion Diagrams

 

Acceleration Review

Acceleration - the time rate of change in velocity  

 

a = ∆V/∆t = (Vf - Vi)/t

 
Uniform Acceleration?

 

 

 

- constant  change
in velocity per unit time

 

 

Which data shows uniform acceleration? Why?



time (sec) Velocity (m/s)
0 5
1 7
2 9
3 11
4 13
time (sec) Velocity (m/s)
0 5
1 10
2 14
3 20
4 30

 

 

 

Left Data Shows Constant Acceleration

a = ?

 

 

a = 2 m/s2

 

 

Describe the motion

Ex)

Step 1 - y changes?

 

Step 2 - Slope = ∆y/∆x =

 

 

 

Answers

Step 1 - y changes: - Velocity is increasing

 

Step 2 - Slope = ∆V/∆t  = a

acceleration is constant +

 

 

Prove this is constant acceleration

  

Every 2 seconds
the object gains
exactly 15 m/s

 

 

Find the acceleration 

 

 

a = ∆V/∆t

 

(15 m/s)/2 sec 

 

 

a = 7.5 m/s2

 

 

 

 

 

Slope of a V vs. t plot

Slope = ∆y/∆x

= ∆V/∆t = a

 

Ex)

Describe motion using
y axis and slope

Step 1: y axis:

Step 2: Slope

 

Answers

Step 1: y axis: V constant

 

 

Step 2: Slope = ∆V/∆t  = a

a = 0

 

 

 

Ex) Largest acceleration?

January 2001 Regents

 

 

 

 

D - greatest slope

 

 

Ex 4)

Step 1: y axis:

 

 

Step 2: Slope

 

Answers

 

Velocity is Decreasing,

 

Acceleration is
constant
, negative

 

 

Calculate the acceleration

 

 

a = (Vf- Vi)/t

 

 

 (15 m/s - 45 m/s )
    (8 sec - 2 sec)

 

 

 

= -5 m/s2

 

 

Ex 5) Describe the motions

Velocity (m/s)

   

Step 1: y axis:

Step 2: Slope

 






Answers

Step 1: y axis:  V increasing

 

 

Step 2: Slope = ∆V/∆t  = a

a is increasing

 

Ex) Describe the motions

 

Step 1: y axis:

Step 2: Slope

 

 

 

 

 

Step 1: y axis: d increasing

Step 2: Slope = d/t = V

 

Velocity is increasing smoothly

 Acceleration is constant & Positive

 

Non-Uniform Acceleration

 

Ex)

Describe motions

Step 1: y axis:

Step 2: Slope

 

 

 

 

 

Step 1: y axis: d increasing

Step 2: Slope = d/t = v

Velocity is Decreasing smoothly

(slope)

 

Acceleration is

constant & negative

 

 

 

 

Describe motions

d (cm)

Step 1: y axis:

Step 2: Slope

 

 

 

Step 1: y axis: d constant

Step 2: Slope = d/t = v

 

v = 0 (slope)

a = 0

 

 

 

 

Analyzing Motion Plots
St. Mary's H.S.

 

 

 

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