Chapter 2. Motion in Chapter 2. Motion in One DimensionOne Dimension

TerminologyTerminology Mechanics Mechanics : Study of objects in motion.

Kinematics :Kinematics : Description of HOWHOW objects move. (Chapters 2 & 4)

No reference to WHYWHY objects move. Dynamics :Dynamics : WHY objects move. Introduction of the concept of

FORCE!!!FORCE!!! (Most of the course after Chapter 5)

Terminology, contTerminology, cont Translational Motion:Translational Motion: Motion

with no rotation. Rectilinear Motion:Rectilinear Motion: Motion in a

straight line path. Particle Model (Moving Particle Model (Moving

Object):Object): Point-like object. An object with mass and neglected size.

Vectors and ScalarsVectors and Scalars Vector quantitiesVector quantities need both

magnitudemagnitude (size or numerical value) and directiondirection to completely describe them. Will use ++ and –– signs to indicate

vector directions Scalar quantitiesScalar quantities are completely

described by magnitudemagnitude only!!

2.1 Position, Velocity, 2.1 Position, Velocity, SpeedSpeed

Defined in terms of a frame of referenceframe of reference One dimensional, so

generally the x-x- or or y-y-axisaxis

The object’s object’s positionposition is its location with respect to the frame of reference

Active Figure 2.1Active Figure 2.1

(SLIDESHOW MODE ONLY)

Position-Time GraphPosition-Time Graph The position-time

graph shows the motion of the particle (car)

The smooth curve is a guess as to what happened between the data points

DisplacementDisplacement Displacement Displacement (vectorvector):: change in

position during some time interval Represented as

(2.1)(2.1)

SI unitsSI units are meters (m)(m) xx can be positive or negative

DistanceDistance traveled by the object ≠≠ DisplacementDisplacement of the object!!!

x

f ix x x

Average VelocityAverage Velocity The average velocityaverage velocity (vectorvector): rate

at which the displacement occurs

(2.2)(2.2) The dimensionsThe dimensions are length / time

[L/T][L/T] SI unitsSI units are (m/s)(m/s) Is also the slopethe slope of the line in the

position-vs-time graph

t

xx

t

xvv ifxaverage

Average SpeedAverage Speed Average SpeedAverage Speed is a scalar

quantity same units as velocity

(2.3)(2.3)

The average speed is NOT The average speed is NOT (necessarily) the magnitude of (necessarily) the magnitude of the average velocity!!!!the average velocity!!!!

Total DistanceAverage Speed

Total Time

Example 2.1Example 2.1 DisplacementDisplacement

xx1 1 = 30 m = 30 m xx2 2 = 10 m= 10 m Displacement Displacement is a VECTORVECTOR

10 30 20f ix x x m m m

Example 2.2Example 2.2 Average Velocity Average Velocity & Speed& Speed

Suppose the person walks during 50 seconds.

DisplacementDisplacement

Distance (d) =Distance (d) = 100m 100m Average velocity:Average velocity:

Average Speed: Average Speed:

t

xx

t

xvv ifxaverage

XfXi40 0 40f ix x x m m m

400.8 /

50average x

x mv v m s

t s

total distance 100Average speed 2.0 /

total time 50

mm s

s

2.2 Instantaneous 2.2 Instantaneous Velocity and SpeedVelocity and Speed

Instantaneous Velocity Instantaneous Velocity Limit of the average velocityLimit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero

The instantaneous velocityinstantaneous velocity indicates what is happening at every point of time

Instantaneous VelocityInstantaneous Velocity (Velocity)(Velocity)

The general equation for instantaneous velocityinstantaneous velocity is

(2.4-2.5)(2.4-2.5)

The instantaneous velocity can be positive, negative, or zeropositive, negative, or zero

0limxt

x dxv

t dt

Instantaneous Velocity, Instantaneous Velocity, graphgraph

The instantaneous The instantaneous velocityvelocity is the slopeslope of the line tangent to the xx vs tt curve

This would be the greengreen line

The blueblue lines (average velocityaverage velocity) show that as t gets smaller, they approach the greengreen line

Instantaneous SpeedInstantaneous Speed (Speed)(Speed)

The instantaneous speed The instantaneous speed is the magnitudethe magnitude of the instantaneous velocityinstantaneous velocity

Remember: the average average speedspeed is NOTNOT the magnitude of the average velocityaverage velocity

If an objects moves at uniform uniform velocityvelocity (constant)(constant),, then: Instantaneous velocityInstantaneous velocity and average average velocityvelocity at any instant (t) are the same.

Instantaneous Instantaneous = = average average

Example 2.3Example 2.3 Instantaneous & Instantaneous & average velocitiesaverage velocities

Are Instantaneous velocityInstantaneous velocity and Average velocityAverage velocity at any instant t the same? NOT ALWAYS!!!!NOT ALWAYS!!!!

Example:Example: A car starts from rest, speed up to 50km/h, remains at that speed for a time. Slow down to 20 km/hr in a traffic jam, the finally stops. Traveling a total of 15 km in 30 min (0.5 hr).

Similar to Question #4 Homework!!!Similar to Question #4 Homework!!!

Example 2.4Example 2.4 Instantaneous Instantaneous & average velocities& average velocities

Example 2.4 Example 2.4 Instantaneous & Instantaneous & average velocities, contaverage velocities, cont

15Average velocity 30.0 /

0.50

x kmkm h

t h

Examples to Read!!!Examples to Read!!! Example 2.2Example 2.2 (Page 30) Example 2.3Example 2.3 (Page 30)

Homework Problems to be Homework Problems to be solved in Class!!!solved in Class!!! Problem: 3Problem: 3 Problem: 6Problem: 6

Material for the Material for the MidtermMidterm