CH4 Linear Motion with Uniform Acceleration

CH4 Linear Motion with Uniform Acceleration

Physics (A) Winter, 2010-2011Physics (A) Winter, 2010-2011

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Relative MotionRelative Motion An object is moving if its position

relative to a fixed point is changing.Ex. Are you moving when:

• you are sitting in a moving car?• ANS. YES, relative to ground NO, relative to the driver’s seat

• running down the street?• ANS. YES, relative to the ground

NO, relative to your shoes• you are watching a city bus drive by?

• ANS. NO, but the bus is relative to you/ground

NO, but the passengers are relative to you/ground 2

SpeedSpeed• Speed = change in distance/change in time• Symbol is v• Units: m/s “meters per second” / sign = per• Scalar Quantity: a # with NO DIRECTION• SAME AS VELOCITY BUT IGNORE DIRECTION!• Ex. You drove 40 mi/hr this morning on Eureka

Rd

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VelocityVelocity• Velocity = change in distance/change in time• Symbol is v • Units: m/s “meters per second” / sign = per• Vector Quantity: value has magnitude AND

direction (N,S, up, down, etc.)• SAME AS SPEED BUT DIRECTION MATTERS!• Ex. You drove 40 mi/hr eastbound this morning

on Eureka Rd

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Speed & VelocitySpeed & Velocity• Speed/Velocity - the rate of change in

position over time (distance/time)• Instantaneous speed: Your

speedometer• Average speed:

vavg: Δ d (Eq. 5)

Δ t• Ex. You traveled from Southgate to

Westland (18 mi) in 1 hour, for an avg. speed of 18 mi/hr

• How is velocity different from speed?5

Change in Velocity

Change in Velocity

• What causes an object to change velocity?

• 3 THINGS CAN CAUSE IT:1. Change in Speed2.Change in Direction3.Change in BOTH

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AccelerationAcceleration• Acceleration = change in velocity/change in

time• Symbol is a• Units: m/s2 “meters per second squared” • Vector Quantity: value has magnitude AND

direction (N,S, up, down, etc.)• Ex. You accelerated at 4 m/s2 eastbound this

morning on Eureka Rd• Can be positive or negative, accels = positive,

decels = negative• Uniform Acceleration=constant acceleration

Ex. g=9.8 m/s2 7

Kinematic Equations for Uniform Acceleration

Kinematic Equations for Uniform Acceleration

vf = vi + a∙t (Eq. 6)

∆d = ½(vf+vi)t (Eq. 7)

∆d=vi∙t + ½∙a ∙t2 (Eq. 8)

vf2=vi

2 + 2∙a∙d (Eq. 9)

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DeltaDelta∆ is “Delta” on greek alphabet. It means “difference”

∆ gives you the right to subtract. In Science,

∆ = Final - Initial 9

Free FallFree Fall

• Free Fall = object is under the influence of force of gravity ONLY

• Elapsed Time (ET) = Δt=time an object starts to fall/move to time object stops to fall/move

• All objects fall on Earth at a=g=9.8 m/s2

• NEVER NEVER NEVER ESTIMATE/APPROXIMATE g!!!!!!! 10

Air ResistanceAir Resistance• When an object falls, is the

force of gravity, the only force acting on the object?

• NO! Air resistance, a form of friction, is acting in OPPOSITE direction of force of gravity

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Graphs of Motion-Velocity

Plot

Graphs of Motion-Velocity

Plot

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Graphs of Motion-Velocity

Plot

Graphs of Motion-Velocity

Plot• Graph is Linear (straight line)• Slope = m = rise

run• Slope of Speed/Velocity Graph

= CONSTANT ACCELERATION, a

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Graphs of Motion-Distance

Plot

Graphs of Motion-Distance

Plot

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Graphs of Motion-Distance

Plot

Graphs of Motion-Distance

Plot• Graph is NON-linear (parabola)• Slope = m = rise

run• Slope of Distance Graph =

INSTANTANEOUS SPEED, v

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Math PracticeMath Practice Ex. If your average speed is 40 km per

hour and you have traveled for 0.5 hour, what distance have you traveled?

GIVEN:Vavg = 40 km/hΔt = 0.5 h

UNKNOWN: Δd = ?EQUATION: Vavg = Δ d

Δ tPLUG-IN: 40 km/h = Δ d

0.5hSOLVE: Δd = 20 (km)

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Problem Solving Flashcard!Problem Solving Flashcard!1. Circle what the question is asking you to find

(less than 3 words!). Put the symbol for this phrase under Unknown: section.

2.Read problem and list all of your GIVENS as their symbols NOT words under GIVEN: section.

3.Go to your formula sheet and pick a formula that has ALL GIVENS AND UNKNOWN in it. Write it under FORMULA: section.

4.Under PLUG-IN: section, plug-in what you know (from GIVENS and UNKNOWN) EXACTLY WHERE YOU FIND IT IN FORMULA.

5.Using Algebra, solve for missing variable with units, under the SOLVE: section.

6.Circle your answer.

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