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**A Study of Speed, Velocity and Acceleration**

Motion A Study of Speed, Velocity and Acceleration

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**To describe motion accurately a**

FRAME OF REFERENCE is necessary. A FRAME OF REFERENCE is a system of objects that are not moving with respect to one another.

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What is Motion? When an object changes position in relation to a FRAME OF REFERENCE (an object that is not moving) we say that the object is in motion For example, a car is in motion when it changes its position with a FRAME OF REFERENCE such as a tree.

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When describing motion it is helpful to be able to describe how far an objected moved and which direction the object moved in.

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**Distance is the length of a path between two points.**

The distance of this car traveled on the track is 50 cm.

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Displacement is the direction from the starting point and the length of a straight line from the starting point to the ending point.

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Distance and Displacement are similar but not the same.

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**Distance is either zero**

or a positive value.

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**Displacement uses positive and negative numbers.**

Positive numbers are for displacement to the right of the origin & Negative numbers are for displacement to the left the origin.

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**Distance Vs. Displacement**

5 km Distance: how far something actually traveled total (25km) Displacement: the length of the straight line between the starting and stopping points (11km) 10 km 11 km 10 km

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Displacement = ? Diner from home is 15 km Total Distance = ?

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25km Displacement = 21km 15 km Total Distance = ? 5 km 15 km

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Displacement = ? 10 km 5 km Total Distance = ?

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**How many steps did it take to walk around the room?**

Where do you end up on his walk?

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**Speed Speed describes how fast an object is moving**

If an object is not moving it has no speed

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**Instantaneous speed A speedometer shows a car’s instantaneous speed.**

The instantaneous speed is the actual speed an object has at any moment.

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**When an object is covering an equal distance **

in an equal amount of time, it is moving at a constant speed Most objects do not travel at constant speed

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**When you divide the total distance of a trip by the time taken you get the average speed.**

On this driving trip around Chicago, the car traveled and average of 100 km/h.

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Speed The speed of a moving object is usually different at any given moment, so we must calculate the average speed Average Speed (V) = Distance (D) Time (T) Units= m/s D V T

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**distance units over time units.**

The units for speed are distance units over time units.

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**to mean speed with direction.**

We use the term velocity to mean speed with direction.

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**Velocity describes the speed and direction of an object**

i.e. The car was moving with a velocity of 25m/s east Velocity (V) = Distance (D) Time (T) Units= m/s + direction

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**Graphs of Motion Constant speed means the speed stays the same.**

An object moving at a constant speed always creates a position vs. time graph that is a straight line.

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**Speed can be represented in a Position(distance)-time graph**

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**Time is the independent variable because time will pass whether distance is traveled or not**

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Distance is the dependent variable because the distance traveled depends on how much time an object is moving

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**A position vs. time graphs can compare the motion of different objects.**

The steeper line on a graph means a faster speed.

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**The slope of a line is the ratio of the “rise” to the “run”.**

The steepness of a line is measured by finding its slope. The slope of a line is the ratio of the “rise” to the “run”.

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**Most objects do not move at a constant speed**

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**Acceleration is the rate at which your speed**

(or velocity) changes. If your speed increases by 1 meter per second (m/s) for each second, then your acceleration is 1 m/s per second.

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**Acceleration occurs whenever there is a change in speed, direction, or both.**

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**The word “acceleration” is used for any change in speed, up or down.**

Acceleration can be positive or negative.

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**Positive acceleration adds more speed each second.**

Things get faster. Speed increases over time.

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**The position vs. time graph is a curve when there is Positive Acceleration.**

The car covers more distance each second, so the position vs. time graph gets steeper each second.

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**Negative acceleration subtracts some speed each second.**

Things get slower. People sometimes use the word deceleration to describe slowing down.

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**When a car is slowing down, the speed decreases so the car covers less distance each second.**

The position vs. time graph gets shallower with time.

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**Acceleration describes how quickly speed changes.**

Acceleration is the change in speed divided by the change in time.

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Acceleration Acceleration is any change in velocity (a change in speed and/or direction) Acceleration=Final Velocity-Initial Velocity Time a = Vf-Vi t Units= m/s2

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**(non-zero speed) and have no acceleration (think cruise control).**

You can be moving (non-zero speed) and have no acceleration (think cruise control). You can also be accelerating and not moving! A falling object begins accelerating the instant it is released.

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**An object is in free fall**

if it is accelerating due to the force of gravity and no other forces are acting on it.

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**The letter “g” is used for acceleration due to gravity.**

Falling objects increase their speed by 9.8 m/s every second, or 9.8 m/s2 The letter “g” is used for acceleration due to gravity.

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