# Kinematics: What is velocity and acceleration?

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Kinematics: What is velocity and acceleration?

Let’s Review Distance traveled (m) Average Velocity (m/sec) v = d t Time taken (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 x t v a t t x

Motion Graphs x v a t t t x Starting Point Direction Velocity Acceleration + Positive + V (speeding up) +constant

Acceleration Example #1
V (m/s) a (m/s/s) Δv from +5 to +10 m/s requires a +5 m/s/s acceleration!

Motion Graphs x v a t t t x Positive (+) +V (slowing down) -constant
Starting Point Direction Velocity Acceleration Positive (+) +V (slowing down) -constant

Acceleration Example #2
V (m/s) a (m/s/s) Δv from +10 to + 5 m/s requires a - 5 m/s/s acceleration!

Motion Graphs x v a t t t x Starting Point Direction Velocity Acceleration above negative (-) -V (speeding up) -constant

Acceleration Example #3
V (m/s) a (m/s/s) Δv from -5 to -10 m/s requires a -5 m/s/s acceleration! Direction is negative (-), velocity is increasing (+) Therefore acceleration is (-)

Motion Graphs x t a v t t x above negative (-) - V (slowing down)
Starting Point Direction Velocity Acceleration above negative (-) - V (slowing down) +constant

Acceleration Example #4
V (m/s) a (m/s/s) Δv from -10 to -5 m/s requires a +5 m/s/s acceleration! Direction is (-), velocity is slowing down (-) Therefore acceleration is (+)

Summary of Velocity & Acceleration
+ - Moving positive direction; Speeding up + acceleration Moving negative direction; Slowing down - acceleration Moving positive direction; Slowing down Moving negative direction; Speeding up

Action/Sign of Velocity Decreasing speed + direction
Determining signs for velocity and acceleration Direction of Motion Action/Sign of Velocity Sign of Acceleration Increasing speed + direction + Decreasing speed + direction - Increasing speed - direction - + Decreasing speed - direction

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