mathematical model of motion chapter 5. velocity equations average velocity: v = d/ t to find the...
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Velocity Equations
Average velocity: v = d/t To find the distance traveled with constant
or average velocity : d = vt To find an object’s location along the x
axis: x = x0 + vt
Constant Acceleration Equations
Final velocity after acceleration: v = v0 + at
Final position after acceleration d = ½ (v + v0)t
d = v0t + ½at2
Final velocity after acceleration v2 = v0
2 + 2a(d)
Free FallFree Fall
Objects accelerate as they fall Acceleration due to gravity is
9.80 meters per second per second
g = 9.80 m/s2
So speed of falling object increases almost 10 m/s every second it falls
Free Fall CalculationsFree Fall Calculations Instantaneous speed of
falling object = gt acceleration times the elapsed time of fall
To find distance of fall, d = 1/2 gt2
In any time interval, distance fallen = avg. speed times elapsed time
Terminal Velocity
Air resistance slows objects, depending on surface area and air density
Terminal velocity (speed) is reached when force of air resistance equals force due to gravity
In vacuum, all objects fall at same rate
Graphing Motion: position vs. time
Plot position (dependent variable) versus time (independent variable)
Sometimes d is used to represent position In horizontal motion, x is often used
instead To find position at any time, read the
values off the graph using the line
Graphing Motion: Position Graph with 2 or more objects
Motion for two or more objects can be plotted on the same graph
Where lines cross, objects are at the same position
Graphing Motion: Position Graph with Uniform Motion
Equal displacements in equal time intervals
Produces linear graph Slope of position graph gives velocity Horizontal line means zero velocity Upward slope means positive velocity Downward slope means negative velocity
Graphing Motion: Position Graph with Acceleration
Graph will be curved Constant acceleration gives parabola Slope of graph at any point gives
instantaneous velocity
Velocity vs Time Graphs
Plot velocity as dependent variable, time as independent variable
Constant velocity gives horizontal line Slope of graph gives acceleration Positive acceleration gives upward slope Negative acceleration slopes downward If graph is linear, acceleration is constant
Velocity vs Time Graphs: Finding Displacement
Displacement can be found from velocity graph by finding the area between the graph and the time axis
Divide the area bounded by the graph line, the horizontal axis and the initial and final times into geometric sections (squares, rectangles, triangles) and find the area
Area below the time axis is negative displacement