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Linear Motion Chapters 2 and 3

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**Some Terms Motion Vector quantity Scalar quantity Displacement**

A change in position over time Vector quantity A factor with magnitude and direction Scalar quantity A factor with only magnitude Displacement The change in an object’s position Resultant The net effect of two or more vectors

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Motion Diagrams A series of images (or of points) that show the position of a moving object at equal time intervals SI unit of position is m SI unit of time is s In order to be useful, we need to establish a coordinate system Establish a location to be zero (origin) Establish a direction to be positive (ex. Moving to the right could be positive, moving left would then be negative)

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Motion Continued We can use these diagrams to create vectors showing the displacement of the moving object from its origin to its ending position The direction it points indicates the direction of movement, the length indicates the magnitude We indicate the change in a factor by using the Greek letter delta, (ex. t is the change in time) 2 equations: t = tf – ti d = df – di Remember, the signs for the displacements are based on the coordinate system (they could be negative)

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Graphing Motion You would plot the dependent variable (displacement) on the y axis and the independent variable (time) on the x axis The line created represents the location you’d most likely find the object at any particular time (instantaneous location) You could plot more than one line on the same graph (useful if you want to compare the locations of 2 objects moving in the same space) You’d need to use the same coordinate system for both Where the lines cross, indicate when they are at the same location

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Velocity The rate at which displacement changes with time (a vector quantity) SI unit is m/s Can be found by determining the slope of a line on a position–time graph (rise/run) or using a formula (v = d/ t) The steeper the slope, the faster the object is moving These both find the average velocity over the whole time period, not the instantaneous velocity

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**Speed versus Velocity They are not the same thing**

Velocity is in a particular direction, speed isn’t Speed is a scalar quantity (it cannot be negative), it only indicates magnitude, not direction Remember with our coordinate system, the sign indicates the direction of motion A negative velocity doesn’t mean the object is slowing down, it just means it’s moving in the opposite direction

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Predicting Locations Can predict the location of a moving object by continuing the line of the graph out until the desired time point Can use a variation of the linear graph formula d = vt + di v is the average velocity, t is time and di is initial displacement

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**Acceleration The rate at which velocity is changing with time**

SI unit is m/s2 Occurs because an object speeds up, slows down or changes direction Remember, since velocity is a vector, acceleration is too A negative acceleration doesn’t indicate slowing down, it indicates the direction of acceleration An acceleration of zero doesn’t mean the object isn’t moving, just that it isn’t speeding up or slowing down

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Finding Acceleration Can be done by finding the slope of a velocity-time graph (velocity goes on the y axis, time on the x axis) Can be done using an equation (a = v/ t) As with time and displacement, v = vf - vi As with velocity, these both calculate the average acceleration, not the instantaneous acceleration

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**Using Acceleration to make Predictions**

With a constant acceleration, you can predict a velocity at a given time You can use the graph OR vf = vi +a t With a constant acceleration, you can predict a displacement at a given time You can find the area under the velocity-time graph OR df = di + vitf + 1/2a(tf)2

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**Free Fall Motion of an object due to gravity only (no air resistance)**

Measure to be 9.8 m/s2 for all objects on Earth (regardless of their mass or size) Remember the sign indicates direction so, we often consider it positive if moving toward the Earth and negative if an object has been thrown upward All the same formulas and rules apply, the acceleration will just always be 9.8 m/s2

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Projectile Motion Results from a combined effect (resultant) of horizontal velocity and vertical velocity (ie gravity) The resultant path is curved The horizontal velocity remains constant (a = 0) if no air resistance The vertical velocity is changing due to gravity (a = 9.8 m/s2) For any 2 angles of release that add to 90o, the range is the same (horizontal distance traveled) But the bigger angle will remain airborne for longer

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A Mathematical Model of Motion

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