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Linear Motion Chapters 2 and 3. Some Terms  Motion  A change in position over time  Vector quantity  A factor with magnitude and direction  Scalar.

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Presentation on theme: "Linear Motion Chapters 2 and 3. Some Terms  Motion  A change in position over time  Vector quantity  A factor with magnitude and direction  Scalar."— Presentation transcript:

1 Linear Motion Chapters 2 and 3

2 Some Terms  Motion  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

3 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)

4 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 = t f – t i   d = d f – d i  Remember, the signs for the displacements are based on the coordinate system (they could be negative)

5 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

6 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

7 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

8 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 + d i  v is the average velocity, t is time and d i is initial displacement

9 Acceleration  The rate at which velocity is changing with time  SI unit is m/s 2  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

10 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 = v f - v i  As with velocity, these both calculate the average acceleration, not the instantaneous acceleration

11 Using Acceleration to make Predictions  With a constant acceleration, you can predict a velocity at a given time  You can use the graph OR  v f = v i +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  d f = d i + v i t f + 1/2a(t f ) 2

12 Free Fall  Motion of an object due to gravity only (no air resistance)  Measure to be 9.8 m/s 2 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/s 2

13 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/s 2 )  For any 2 angles of release that add to 90 o, the range is the same (horizontal distance traveled)  But the bigger angle will remain airborne for longer


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