Chapter 2Chapter 2Motion and SpeedMotion and Speed

Sec. 1 Describing Sec. 1 Describing MotionMotion MotionMotion occurs when an object occurs when an object

changes position.changes position. You don’t need to You don’t need to seesee something something

move to know that motion has move to know that motion has taken place.taken place.–You just need a You just need a reference point reference point to know to know

if motion occurredif motion occurred

Distance and Distance and DisplacementDisplacement DistanceDistance—how far an object moved—how far an object moved

The SI unit for distance is the meter,mThe SI unit for distance is the meter,m DisplacementDisplacement—the distance and —the distance and

direction of an object’s change in direction of an object’s change in position from the starting point.position from the starting point.

Distance Vs Displacement AnimationDistance Vs Displacement Animation

SpeedSpeed RateRate—any change over time—any change over time SpeedSpeed—the distance an object travels per —the distance an object travels per

unit of time.unit of time.Speed = Speed = distancedistance s = s = dd

timetime tt

Suppose you ran 2 km in 10 min, what is Suppose you ran 2 km in 10 min, what is your speed?your speed?s = 2 km / 10 mins = 2 km / 10 min

s = 0.2 km/mins = 0.2 km/min

Graphing MotionGraphing Motion On a distance vs. time graph, time On a distance vs. time graph, time

goes on the x-axis and distance goes goes on the x-axis and distance goes on the y-axis.on the y-axis.

The slope (steepness) of the line The slope (steepness) of the line represents the speed of the object.represents the speed of the object.

Distance

Time↑

Speed

Distance vs. TimeDistance vs. Time

Which one is the fastest?Which one is the fastest? Which one isn’t moving?Which one isn’t moving?

Bubble Gum LabBubble Gum Lab

Speed Challenge Lab/ wkstSpeed Challenge Lab/ wkst

http://www.nsf.gov/news/special_reports/http://www.nsf.gov/news/special_reports/olympics/bobsled.jsp olympics/bobsled.jsp

http://www.nsf.gov/news/special_reports/http://www.nsf.gov/news/special_reports/olympics/mathletes.jsp olympics/mathletes.jsp

Average & Instantaneous Average & Instantaneous SpeedSpeed

Average speedAverage speed—the total distance —the total distance traveled divided by the total time of traveled divided by the total time of travel.travel.–Used when speed is changingUsed when speed is changing

Instantaneous speedInstantaneous speed—the speed —the speed at a given point in time.at a given point in time.–Ex. SpeedometerEx. Speedometer

VVeelloocciittyy Speed describes only how fast Speed describes only how fast

something is moving.something is moving. VelocityVelocity—includes the —includes the speedspeed of an of an

object AND the object AND the directiondirection of its of its motionmotion– Ex: 40 mi/hr North or 5 m/s upEx: 40 mi/hr North or 5 m/s up

Change in VelocityChange in Velocity Velocity can change in 2 waysVelocity can change in 2 ways

1.1. Change in speedChange in speed

2.2. Change in directionChange in direction

Or BothOr Both Ex: a race car has a constant speed Ex: a race car has a constant speed

of 100km/hr around an oval track.of 100km/hr around an oval track.– Speed is constant, but velocity Speed is constant, but velocity

changeschanges

AcAccceleleerarattioionn AccelerationAcceleration: Change in velocity over time: Change in velocity over time

– acceleration = acceleration = change in velocitychange in velocity

timetime

When something When something speeds upspeeds up, it has a , it has a positivepositive acceleration acceleration

When something When something slows downslows down, it has a , it has a negativenegative acceleration acceleration

The slope of a velocity vs time graph is the The slope of a velocity vs time graph is the accelerationacceleration

Units for acceleration are m/s/s or m/sUnits for acceleration are m/s/s or m/s22

ChChaangngiing ng DDirireectctiionon Remember:Remember: A change in velocity A change in velocity

can be either a can be either a change in speed or a change in speed or a change in direction.change in direction.

Any time an object Any time an object changes direction, its changes direction, its velocity changes and velocity changes and it is accelerating.it is accelerating.

Calculating Calculating AccelerationAcceleration As you know,As you know,

– acceleration = acceleration = change in velocitychange in velocity

timetime

Change in velocity = Change in velocity = final velocity (final velocity (vvff) – initial velocity() – initial velocity(vvii))

We can rewrite the acceleration equation as We can rewrite the acceleration equation as a = a = (v(vff – v – vii))

tt

Calculating Calculating PositivePositive Acceleration Acceleration An airplane starts at rest and travels An airplane starts at rest and travels

down a straight runway and reaches a down a straight runway and reaches a top speed of 80 m/s in 20 s. What is its top speed of 80 m/s in 20 s. What is its acceleration?acceleration?– a = a = (v(vff – v – vii)) = = (80 m/s – 0 m/s)(80 m/s – 0 m/s)

tt 20 s20 s

= 4 m/s= 4 m/s22

The airplane is speeding up, so the The airplane is speeding up, so the acceleration is positive.acceleration is positive.

Velocity vs Time Graph Velocity vs Time Graph of Positive Accelerationof Positive Acceleration

Calculating Calculating NegativeNegative Acceleration Acceleration

A skateboarder is moving at 3 m/s A skateboarder is moving at 3 m/s and comes to a stop in 2 s. What is and comes to a stop in 2 s. What is the acceleration?the acceleration?a = a = (v(vff – v – vii)) = (0 m/s – 3 m/s) = -1.5 = (0 m/s – 3 m/s) = -1.5

m/sm/s22

t 2 st 2 s

The skateboarder slowed down, so The skateboarder slowed down, so the acceleration is negative.the acceleration is negative.

Velocity vs Time Graph Velocity vs Time Graph of Negative Accelerationof Negative Acceleration

Zero AccelerationZero Acceleration When an object has a constant When an object has a constant

velocity, it has 0 acceleration.velocity, it has 0 acceleration.

An Object Changing AccelerationAn Object Changing Acceleration

How Stuff Works: Roller Coaster & The How Stuff Works: Roller Coaster & The Human BodyHuman Body