1. Motion in One Dimension
Acceleration

2. What We Need To Know
What is acceleration?
How are the directions of velocity and acceleration related to the actual motion of an object?
How are displacement, velocity, time, and acceleration related?

3. What We Know Δx v = t What is displacement?
Straight line from where you start to where you end.
Positive and negative numbers tell us what?
Direction
What is the difference between scalars and vectors?
Both have magnitude, but only vectors have direction.
How do you determine velocity?
v = Δx t

4. Average Velocity xi x ti xf tf t
Time
Position xi x ti
Rise over run… the slope of a position time graph gives velocity xf tf t

6. Changing Velocity
If either an object’s velocity or direction are changing then the object’s velocity is changing.

7. Acceleration
Acceleration (a) is the rate of change of velocity over time. How fast velocity is changing.
Acceleration
or… =
change in velocity
time interval
_____________
_____ t
vf - vi a =
___ t ∆v a =

8. Instantaneous VelocityVi Vf
Just like position, we can identify the object’s velocity at any instant by reading a clock
At ti, the velocity is vi … At t , the velocity is v

9. Velocity vs. Time Graphs
On a velocity vs. time graph, you can determine graphically an objects velocity at any given time (instantaneous velocity)
Time
Velocity

10. Discuss + is right, - is left
Which direction is the object moving at A?
At which point(s) is acceleration occurring?
At which point(s) is there constant velocity?
What is happening at D? 10 C
Velocity B A
Time D
-10

11. Average Acceleration vf vi ti tf
Time
Velocity ti vi t2 v2 . tf vf
We can use instantaneous velocity and time to help understand how an object’s velocity changes over time.
Velocity vf vi
The slope of a velocity vs. time graph gives acceleration ti tf
Time

12. Acceleration and Displacement
The slope of the velocity versus time graph represents acceleration
Velocity
How do you find area under the graph? (It’s a triangle)
The area is a function of velocity multiplied by time V t v
How do we figure out area? ½ base times width, so ½ v times t. Wait hold on to that.
Have v = Δx/t on the board so I can show Δx = vt
The area under the velocity versus time graph represents displacement t
Time

13. Displacement and Acceleration Constant Acceleration
Area = ½ (vf – vi)t + vi . t Vi t Vf
We know the area represents displacement, so….
Δx = ½ (vf - vi)t + vit
or,
Dx = ½ (vf + vi)t

14. Constant Acceleration
Equations:
Symbol
Variable
Units Δx
displacement m v
velocity
m/s t
time s a
acceleration
m/s2
∆x = (vf + vi)t 1 _ 2
∆x = vit + at² 1 _ 2
vf² = vi² + 2a∆x

15. Acceleration and Direction
Displacement, Velocity, and Acceleration must have a magnitude and direction
In 1-D, direction is positive or negative
Will displacement, velocity, and acceleration always go in the same direction (same sign)? -1 1 2 3 4 5 6
X (meters) + -

16. Velocity vs Acceleration
Object’s Motion +
Speeding Up in the positive direction -
Slowing Down in the positive direction
Speeding Up in the negative direction
Slowing Down in the negative direction
-/+
Speeding Up from at rest
At Rest

17. Graphs of Constant Acceleration
distance
velocity
acceleration
time

18. Example
An aircraft has liftoff speed of 120 km/h. What is the minimum acceleration required if the aircraft needs to be airborne after 240m?
If a car initially traveling at 5 m/s accelerates at a rate of 3.0 m/s2:
What was the car’s final speed after 8 seconds?
How far did the car travel?

19. What We Now Know
What is acceleration?
How are the directions of velocity and acceleration related to the actual motion of an object?
How are displacement, velocity, time, and acceleration related?