physics chapter 2 motion in one dimension
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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
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
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
position time graph
Steeper slope = larger velocitySteeper slope = larger velocity
position time
What does this graph mean?
position
time
Instantaneous velocity = tangent line of the slope
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
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
3. The slope and shape of a 3. The slope and shape of a graph graph
describes the objects motiondescribes the objects motionvelocity
Time
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
2. Displacement with Constant 2. Displacement with Constant AccelerationAcceleration
ΔΔ x = ½ (v x = ½ (vii + v + vff) ) ΔΔtt
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
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
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
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