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

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therefore therefore ΔΔx/ x/ ΔΔt =vt =vi i +v +vff

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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