Kinematics in One Kinematics in One DimensionDimension

Pgs. 19-37Pgs. 19-37

MECHANICS: the study of the MECHANICS: the study of the motion of objects & related forces. motion of objects & related forces.

Two divisions of mechanics:Two divisions of mechanics:

KinematicsKinematics: describe HOW objects move: describe HOW objects move DynamicsDynamics: deals with forces & WHY : deals with forces & WHY

objects moveobjects move

Translational MotionTranslational Motion In chapter 2, we In chapter 2, we

will only discuss will only discuss objects that move objects that move withoutwithout rotating. rotating.

This type of motion This type of motion is called:is called:TRANSLATIONAL TRANSLATIONAL

MOTIONMOTION

REFERENCE FRAME REFERENCE FRAME

Any measurement of position, Any measurement of position, distance, or speed must be distance, or speed must be made with respect to a made with respect to a frame frame ofof referencereference..

Reference frame or Frame of Reference frame or Frame of ReferenceReference

A person walks 5 km/h. The train is A person walks 5 km/h. The train is moving at 80 km/h with respect to moving at 80 km/h with respect to the ground. How fast is the person the ground. How fast is the person going with respect to the ground?going with respect to the ground?

Specifying the Motion of an ObjectSpecifying the Motion of an Object We often specify the We often specify the

motion of an object by motion of an object by using a set of coordinate using a set of coordinate axes. This can axes. This can represent our frame of represent our frame of reference.reference.

For one dimensional For one dimensional motion, we choose the motion, we choose the x-axis as the line along x-axis as the line along which motion takes which motion takes place.place.

If an object is dropped, If an object is dropped, motion is vertical and motion is vertical and we use the y-axis.we use the y-axis.

DISTANCE vs. DISPLACEMENTDISTANCE vs. DISPLACEMENT Distance traveled here is not the same as Distance traveled here is not the same as

the DISPLACEMENT!the DISPLACEMENT! Displacement is the change in postion of Displacement is the change in postion of

the object or how far the object is from its the object or how far the object is from its starting position.starting position. Total distance

traveled?100 m

Total displacement?

40 m

Let’s say you go 50 m east.Let’s say you go 50 m east.

Then you go 10 m south

50 m east

10 m south

You have gone a distance of 60 m, but your displacement is less than that! You could find it by using the Pythagorean Theorem. Where the displacement is equal to the hypoteneuse.

Displacement is a vector.Displacement is a vector.

Displacement has Displacement has BOTHBOTH magnitude & magnitude & direction. Vectors are represented with direction. Vectors are represented with arrows.arrows.Displacement is represented with an X since it is along the x-axis. Displacement is then “the change in x” or x

Positive DisplacementPositive Displacement Change in Change in

displacement isdisplacement is

x = xx = x22 – x – x11

= 30 m – 10 m= 30 m – 10 m

= 20 m= 20 m

Negative DisplacementNegative Displacement The person is The person is

walking in the walking in the oppositeopposite direction direction on the x-axis nowon the x-axis now

x = xx = x22 – x – x11

= 10 m – 30 m= 10 m – 30 m = = -- 20 m 20 m

The negative value here simply indicates a direction! (to the left)

SPEED VS. VELOCITYSPEED VS. VELOCITY SpeedSpeed is a SCALAR quantity. It is is a SCALAR quantity. It is

defined as the total defined as the total distancedistance traveled divided by the time it takes traveled divided by the time it takes to travel this distance. to travel this distance.

s = total distance/total times = total distance/total time VelocityVelocity is a VECTOR quantity. It is is a VECTOR quantity. It is

defined in terms of defined in terms of displacementdisplacement rather than total distance.rather than total distance.

VELOCITYVELOCITY

AVG AVG = = TOTAL TOTAL DISPLACEMENTDISPLACEMENT

VELOCITYVELOCITY TIME ELAPSEDTIME ELAPSED

v = v = xxtt

Velocity is a function of timeVelocity is a function of time TopTop: car is : car is

traveling at a traveling at a constantconstant velocity. velocity.

BottomBottom: car is : car is traveling with a traveling with a varyingvarying velocity velocity