physics chapter 2 motion in one dimension
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Physics Chapter 2 Motion in One Dimension. I. Displacement & Velocity A. Displacement: change in position 1. displacement not equal to distance traveled 2. displacement = change in position - PowerPoint PPT PresentationTRANSCRIPT
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Physics Chapter 2Physics Chapter 2Motion in One DimensionMotion in One Dimension
I. Displacement & VelocityI. Displacement & Velocity A. Displacement: change in positionA. Displacement: change in position
1. displacement not equal to distance 1. displacement not equal to distance traveledtraveled
2. displacement = change in position2. displacement = change in position
= final position – initial = final position – initial position position
= = ΔΔ x = x x = xf f - x- xi i 3. displacement can be positive or negative3. displacement can be positive or negative
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B. Velocity: how fast something is B. Velocity: how fast something is movingmoving
1. V1. Vavg avg = = ΔΔx x ΔΔtt
= = change in positionchange in position = = displacementdisplacement
change in time time intervalchange in time time interval
2. Not the same as speed, velocity has 2. Not the same as speed, velocity has directiondirection
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3. Velocity can be interpreted 3. Velocity can be interpreted
graphicallygraphically Slope = rise/run = Slope = rise/run = change in vertical coord.change in vertical coord.
change in horizontal change in horizontal coord.coord.
vvavg.avg. = = ΔΔxx
ΔΔ t t
slope = average velocityslope = average velocity
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position time graph
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Steeper slope = larger velocitySteeper slope = larger velocity
position time
What does this graph mean?
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position
time
Instantaneous velocity = tangent line of the slope
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II. AccelerationII. Acceleration
A. Changes in VelocityA. Changes in Velocity 1. Acceleration measures changes 1. Acceleration measures changes
in velocityin velocity
aaavg avg = = ΔΔv/v/ΔΔtt
= v= vff - v - vii
ttff - t - tii
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2. Acceleration has direction & 2. Acceleration has direction & magnitudemagnitude
If If ΔΔv is positive = acceleration is v is positive = acceleration is positivepositive
If If ΔΔv is negative = acceleration is v is negative = acceleration is negativenegative
When velocity is constant,When velocity is constant,
acceleration is 0acceleration is 0
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3. The slope and shape of a 3. The slope and shape of a graph graph
describes the objects motiondescribes the objects motionvelocity
Time
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B. Motion with Constant B. Motion with Constant AccelerationAcceleration 1. Displacement depends on 1. Displacement depends on
acceleration, initial velocity & time.acceleration, initial velocity & time.
vvavgavg = =ΔΔx/ x/ ΔΔtt
vvavgavg =v =vi i +v +vff
22
therefore therefore ΔΔx/ x/ ΔΔt =vt =vi i +v +vff
22
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2. Displacement with Constant 2. Displacement with Constant AccelerationAcceleration
ΔΔ x = ½ (v x = ½ (vii + v + vff) ) ΔΔtt
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3. Final velocity depends on initial 3. Final velocity depends on initial velocity, acceleration & timevelocity, acceleration & time
vvff = v = vii + a + aΔΔtt
Displacement with Constant Displacement with Constant Accl.Accl.
ΔΔx =vx =vi i ΔΔt t +1/2a(ΔΔt )t )22
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4. Time can be found from 4. Time can be found from displacement & velocitiesdisplacement & velocities
ΔΔt = 2 t = 2 ΔΔxx vvi i +v+vff
Final velocity after any displacementFinal velocity after any displacement
VVff2 2 =v=vii
2 2 +2a+2aΔΔxx
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III. Falling ObjectIII. Falling Object
A. Free FallA. Free Fall 1. Free falling bodies undergo 1. Free falling bodies undergo constant accelerationconstant acceleration
9.81m/s9.81m/s22