kinematics: what is velocity and acceleration? lets review v = d t distance traveled (m) time taken...

Kinematics:What is velocity and

acceleration?

Let’s Review

v = d t

Distance traveled (m)

Time taken (sec)

Average Velocity (m/sec)

Instantaneous Velocity: the speed at any given moment (like what your speedometer shows)

Slope of Position vs Time graph is the Average Velocity

The slope of a line is the ratio of the “rise” (vertical change) to the “run”(horizontal change) of the line.

Constant Speed

On a Velocity vs Time graph constant velocity is a straight line

Area under the velocity vs time graph is equal to the distance travelled.

What is a Motion Diagram?

Motion Diagram: Is a more sophisticated dot diagram that conveys more information about the situation.

•What do the arrows indicate?

•What does the length of each arrow indicate about the motion of the object?

Change in Velocity

What must you do to the first velocity arrow to get the second velocity arrow? What direction? How much?

•The arrow you drew to show the difference between the velocity arrows is called a ∆v or change in velocity arrow.

•What does the ∆v arrow tell you about the motion of the object?

Let’s Try!

Lesson 11: Speeding Index

Motion of a Falling Object

Using the video of the falling object we have collected the following data:

Draw a motion diagram.Plot a position time graph.Does this object represent an object with constant

velocity? Explain how you know.

What is Acceleration?

Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity

There are 3 types of acceleration: If an object is increasing in speed (+ acceleration) If an object is decreasing in speed (- acceleration, also called

deceleration) Or if the object changes direction (+ or -)

How do we calculate Acceleration?

Acceleration is the change in speed over the change in time.The slope of the speed versus time graph is the acceleration.

How to Solve Motion Problems

Rearrange the equation to get final velocity

How do we determine the distance travelled by the object if velocity is changing?

Equations to Remember

Motion Graphs

0

av

tt

x

t

x

Motion Graphs

0

x av

ttt

x

Starting Point Direction Velocity Acceleration

0 + Positive + V (speeding up) +constant

Acceleration Example #1

Δv from +5 to +10 m/s requiresa +5 m/s/s acceleration!

V (m/s) a (m/s/s)

0 +5

+ 5 + 5

+10 + 5

15 + 5

Motion Graphs

0

av

ttt

x

x

Starting Point Direction Velocity Acceleration

Positive (+) +V (slowing down) -constant

0

Acceleration Example #2

V (m/s) a (m/s/s)

+ 10 - 5

+ 5 - 5

0 - 5

Δv from +10 to + 5 m/s requiresa - 5 m/s/s acceleration!

Motion Graphs

0

x a

tt

v

t

x

Starting Point Direction Velocity Acceleration

above negative (-)

-V (speeding up) -constant

Acceleration Example #3

Δv from -5 to -10 m/s requiresa -5 m/s/s acceleration!

Direction is negative (-), velocity is increasing (+)Therefore acceleration is (-)

V (m/s) a (m/s/s)

0 -5

- 5 - 5

-10 - 5

-15 - 5

Motion Graphs

0

a

t

x

t

x

v

t

Starting Point Direction Velocity Acceleration

above negative (-) - V (slowing down)

+constant

Acceleration Example #4

V (m/s) a (m/s/s)

- 10 + 5

- 5 + 5

0 + 5

Δv from -10 to -5 m/s requiresa +5 m/s/s acceleration!

Direction is (-), velocity is slowing down (-)Therefore acceleration is (+)

Summary of Velocity & Acceleration

V E L O C I T Y ACCELERATION

+ -

+Moving positive

direction; Speeding up

+ acceleration

Moving negative

direction; Slowing down

- acceleration

-

Moving positive

direction; Slowing down

- acceleration

Moving negative

direction; Speeding up

+ acceleration

Direction of Motion Action/Sign of Velocity

Sign of Acceleration

Determining signs for velocity and acceleration

Increasing speed

+ direction+

Decreasing

speed + direction

-

-

Increasing speed

- direction

Decreasing speed

- direction

+