Mrbscigladstone



Chapter 8: Average Velocity

Section 8.1- The Language of Motion

Direction

• Measuring motion:

- Scalar quantity (scalar)- describes the size of a measurement or the amount (number) being counted, a factor knows as magnitude. Only includes magnitude but no direction.

Example: you walk 4km/h

- Vector quantity (vector)- has both magnitude and direction.

Example: You walk 4km/h [E]

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Distance and Position

• Distance:

- Is a scalar quantity that describes the length of a path between two points or location (d).

- The SI unit for distance is meters, m and it is scalar.

Example: If you skateboard 10km [E] of your home, you travelled a distance of 10km.

• Position:

- Is a vector quantity that describes a specific point relative to a reference point.

- The objects location as seen by an observer from a particular viewpoint.

Example: If you skateboard 10km [E] and return home in a straight line along the same route, your position upon returning is 0km because you are back at your point of origin.

Time and Time Interval

• Time:

- When an event occurs.

- The SI init is s or h.

• Time Interval ∆t:

- The duration of an event.

- Final time minus the initial time.

- Scalar quaintly and the SI unit is s or h.

- To calculate: ∆t= tf – ti

Displacement and Distance

• Displacement ∆d:

- The straight-line distance and direction from one point to another.

- Final position minus the initial position.

∆d = df – di

- How much an object’s position has changed

- The SI unit for displacement is m.

• Directions:

- Are designed as positive or negative using vectors.

- North, east, up and right are positive (+).

- South, west, down and left are negative (-)

Uniform Motion

• Uniform motion:

- Travels equal displacements in equal time intervals.

- Will not speed up or slow down and they would not change direction.

• A Motion Diagram:

- Shows the object’s position at given times and allows us to picture or visualize motion.

- You can identify the position of the ball at corresponding time intervals.

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• Position time graph:

- When you plot the time data on the horizontal axis (x) and the position data on the horizontal axis (y).

- Uniform motion is representing by a straight line on a position-time graph.

• Best-fit line:

- A smooth curve or straight line that most closely fits the general shape outline by the points, to graph real motion.

- Positions and times not given as data can be estimated by finding the location corresponding to a specific time and position on a best-fit line.

Slope

• Slope:

- A slope of a graph refers to whether a lone is horizontal or goes up or down at an angle.

• Positive:

- Slants up to the right indicating that an object’s position, from the origin is increasing with respect to time.

• Zero:

- A zero slope is a straight, horizontal line.

- It represents an object at rest.

• Negative:

- A negative slope slants down to the right, indication an object is mobbing in a negative direction- left, down, west or south.

Section 8.2- Average Velocity

Speed and Velocity

• Speed v:

- The distance an object travels during a given time interval divided by the time interval.

- Speed is a scalar quantity.

- The SI unit for speed is meters per second m/s.

• Velocity:

- The displacement of an object during a time interval divided by the time interval.

- Velocity describes how fast an object’s position is changing.

- The SI init for velocity is meters per second m/s.

• Same Speed, Different Velocities:

- Objects travelling at the same speed can have different velocities.

- Imagine two escalators travelling at the same speed, one going up and the other going down.

- Because they are travelling in opposite directions, one of the directions has a negative sign (which means different velocities.)

• Slope:

- Velocity can be determined from the slope of a position-time graph,

- Slope is calculated- Slope= rise/run or ∆d/∆t

Average Velocity

• Average Velocity:

- The rate of change in position for a time interval.

- It is almost impossible for an object to move at a perfectly uniform rate because of many factors like wind or uneven surface,

- Is a vector and includes a direction.

• Position-time Graph and Average Velocity:

- if moving away from the origin it’s considered positive.

- A positive slope represents the average velocity of the object moving away from the origin.

- A horizontal line, which has zero slope, represents an object at rest.

- A negative slope, represents the average velocity of the object moving back toward the origin.

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Chapter 9: Acceleration

Section 9.1- Describing Acceleration

Changes in Velocity

• Change in Velocity:

- occurs when the speed of an object changes, or its direction of motion changes or both.

- To find changes in velocity, subtract the initial velocity from the final velocity. ∆v = vf – vi

Acceleration

• Acceleration:

- The rate at which an object changes its velocity.

- When talking about acceleration, we need to include the magnitude of the change in velocity of the moving object and need to indicate the change in direction of the object’s velocity.

• Positive and Negative Acceleration:

- When something’s speed is increasing, it has a positive acceleration.

- When something’s speed is decreasing, it has a negative acceleration.

• Declaration:

- Acceleration that is opposite to the direction of motion.

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|Factor |Velocity |Acceleration |

|Increase in speed while travelling forward. Example: |+ Positive |+ Positive |

|accelerating after you have stopped at a stop sign | | |

|Decrease in speed while travelling forwards. Example: |+ Positive |- Negative |

|applying the brakes on a bicycle. | | |

|Increase in speed while travelling backward. Example: a |- Negative |- Negative |

|ball falling to earth. | | |

|No change in speed. Example: running at a constant speed. |Constant |0 |

Direction

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Section 9.2- Calculating Acceleration

Velocity-Time Graphs

• Velocity-Time Graph Represents:

- The motion of an object with change velocity.

- The slope gives the object’s acceleration, which is measured in m/s2.

• Acceleration and best-fit line:

- When a best-fit line passes through all data points, the object’s velocity is changing at a constant rate and the motion is described as constant acceleration.

- However, since not all the velocities may be directly on the best-fit line, the slope is referred to as average acceleration.

Determining Motion from a Velocity-Time Graph:

• If north is considered positive, for lines above the x-axis:

• A positive slope (0 to t1) represents the average acceleration of an object that increases speed at a constant rte while travelling north. Acceleration is constant and positive.

• Zero slope (t1 to t2) represents an object travelling north at a constant speed and it is not accelerating.

• A negative slope (t2 to t3) represents n object that decreases speed at a constant rate while travelling north. Acceleration is constant and negative and velocity is positive.

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Calculations

• Calculating Acceleration:

- For constant acceleration, acceleration is equal to change in velocity divided by the time interval. A= ∆v/ ∆t

• Calculating Change in Velocity and Time:

- For velocity- ∆v= a∆t

- For time- ∆t= ∆v/a

Gravity and Acceleration

• Gravity:

- When an object falls near Earth’s surface, the force of gravity pulls in downwards.

- Consider a ball being thrown straight up into the air (up is +)

- On the way up the ball’s velocity is decreasing. The ball is slowing down so its acceleration is negative.

- At its max height the balls velocity is zero for an instance since the direction of the ball is changing (the ball is still accelerating.)

- When the ball starts to come down, its speed increases. However, its velocity is negative because the ball is heading “down.” The balls acceleration is negative.

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• Gravity and Air Resistance:

- Air resistance is a friction-like force that opposes the motion of objects to move through the air.

- If the object is falling downward, air resistance acts upward on the object.

• Acceleration due to Gravity:

- In the absence of air resistance, all objects, no matter what weight fall with the same constant acceleration of 9.8m/s2 downward.

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