Vectors and ScalarsVectors and Scalars

Scalars and VectorsScalars and Vectors ExampleExample

• If someone asks where Pittsburgh is and I say 35 If someone asks where Pittsburgh is and I say 35 miles from here, will they know how to get there? miles from here, will they know how to get there?

• What else do they need to know?What else do they need to know?• MAGNITUDEMAGNITUDE (Size) and (Size) and DIRECTIONDIRECTION• VECTORVECTOR

Scalars and VectorsScalars and Vectors

ExampleExample• If someone asks how much money I If someone asks how much money I

have and I say $5, will they know how have and I say $5, will they know how much money I have?much money I have?

• MAGNITUDEMAGNITUDE• SCALARSCALAR

Scalars and VectorsScalars and Vectors Scalar Scalar (magnitude)(magnitude)

• SpeedSpeed• DistanceDistance• Age Age

Vector Vector (magnitude & direction)(magnitude & direction)

• VelocityVelocity• DisplacementDisplacement• AccelerationAcceleration

Speed vs. VelocitySpeed vs. Velocity

AverageAverage • A distance of 80 km in a time of 2 hr A distance of 80 km in a time of 2 hr

averages to 40 km/hr even though you averages to 40 km/hr even though you may have gone faster or slower at may have gone faster or slower at momentsmoments

Speed vs. VelocitySpeed vs. Velocity

ConstantConstant• No variation at allNo variation at all

Constant speed Constant speed ISIS different from different from constant velocityconstant velocity• WHY?WHY?

No change in magnitude vs. no change in No change in magnitude vs. no change in magnitude or directionmagnitude or direction

Speed vs. VelocitySpeed vs. Velocity

80 km/hr vs. 80 km/hr due North80 km/hr vs. 80 km/hr due North• InstantaneousInstantaneous

What the speedometer (and compass?) read What the speedometer (and compass?) read at any particular instanceat any particular instance

Directions of AccelerationDirections of Acceleration Traveling ForwardTraveling Forward

• Step on acceleratorStep on accelerator + acceleration+ acceleration

• Step on brakeStep on brake - acceleration- acceleration

Traveling BackwardTraveling Backward• Step on acceleratorStep on accelerator

- acceleration- acceleration

• Step on brakeStep on brake + acceleration+ acceleration

Examples in CarExamples in Car

10 m/s to 60 m/s in 5 seconds?10 m/s to 60 m/s in 5 seconds?• + 10 m/s+ 10 m/s22

60 m/s to 10 m/s in 5 seconds?60 m/s to 10 m/s in 5 seconds?• -10 m/s-10 m/s22

-10 m/s to -60 m/s in 5 seconds?-10 m/s to -60 m/s in 5 seconds?• -10 m/s-10 m/s22

-60 m/s to -10 m/s in 5 seconds?-60 m/s to -10 m/s in 5 seconds?• 10 m/s10 m/s22

a = a = ΔΔv / v / ΔΔt t (m/s(m/s22 or ft/s or ft/s22))

GravityGravity What causes objects like the book and paper to fall?What causes objects like the book and paper to fall?

Remember, without Remember, without air frictionair friction, all fall at the , all fall at the same ratesame rate. . Most problems we have are without air friction – you’ll be told if Most problems we have are without air friction – you’ll be told if

there is air friction.there is air friction.

Let’s Consider Air FrictionLet’s Consider Air Friction

Let’s Consider Air FrictionLet’s Consider Air Friction

20 feet

3 feet

Let’s Consider Air FrictionLet’s Consider Air Friction