Displacement from Velocity Time Graphs

1
Acceleration

• Displacement fromVelocity Time Graphs

2
Calculating displacement from
v vs t graphs

• Draw a velocity vs time graph for an object that
  goes 20 m in 5 s at a constant speed.
• Find the area between the line and the x-axis.

The area under a velocity time graph is the
displacement. This is true for any velocity time
graph.
Area length x width
Area (4m/s)(5s)
Area 20 m
3

• An object moves forward at a constant
  acceleration of 5.0 m/s2 for 10 seconds, starting
  from rest. How far does it go? (draw a v vs t
  graph)

Area
Area
Area
4

• An object starts at 30 m/s and accelerates at 5.0
  m/s2 for 10 s.
• Find the distance it traveled.

Area Area of Triangle Area of Rectangle
Area
Area
Area
5

• A car starts at 20 m/s and accelerates steadily
  at 5.0 m/s2 for 10 seconds. Find the total
  distance it traveled.

a v vo
a 5 m/s2
vo 20 m/s
t
t 10 s
v vo at
v(10s) 20m/s (5.0m/s2) (10s)
v(10s) 70m/s
Area Area of Triangle Area of Rectangle
Area ½(base x height) (length x width)
Area
Area
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General Case
a x t
vo

• An object accelerates from vo at a for t
  seconds. Find d in terms of a, vo, and t.

d ½(base x height) (length x width)
d ½(t x at) (vo x t)
d vot ½ at2
(constant acceleration)
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• Given v, vo, and t. Find the distance.

vav
d (length x width)
d vav x t
vav ½ (v vo)
d vavt
Always true for constant acceleration
8
Examples

• A boy accelerates from rest at a steady 4.0 m/s2.
• How far does he go in 10 seconds?
• How long does it take him to go 1 km?
• How fast is he going after he has covered 500 m?

a 4.0 m/s2
d vot ½ at2
vo 0 m/s
v
t 10 s
t
d
d 1 km
9
d vot ½ at2
a 4.0 m/s2
c) Step 1
t
v
vo 0 m/s
d 500 m
Step 2
v vo at
10

• Find the initial velocity of an object that
  covers 200 m with an acceleration of 4 m/s2 in 5
  seconds.
• How long does it take a dragster with an initial
  velocity of 10 m/s to cover 400 m if it has a
  steady acceleration of 2.0 m/s2?

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Formula Summary
Constant Acceleration Kinematics
v vo at
d vavt
vav ½ (v vo)CONSTANT ACCELERATION ONLY!!
d vot ½ at2
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Assignment

• Homework
• Acceleration Worksheet
• Questions 20-27