MOTION IN TERMS OF POSITION, TIME, AND VELOCITY

DISTANCE VS DISPLACEMENT

MOTION & MOVEMENT ONE-DIMENSIONAL MOTION HAPPENS ALONG A STRAIGHT LINE PATH EXAMPLE A CAR TRAVELLING EAST, WEST, NORTH, OR SOUTH MOVEMENT – A CHANGING POSITION IMAGINE THE CAR AS A SINGLE PARTICLE TRAVELLING ALONG A NUMBER LINE

DESCRIBING CHANGING POSITION (MOTION) SCALARS – DESCRIBE SIZE OR MAGNITUDE, BUT NO INFORMATION CONCERNING THE DIRECTION EXAMPLES A CAR’S ODOMETER DISTANCE = MILES DRIVEN A CAR’S SPEEDOMETER INSTANTANEOUS SPEED OF THE CAR VECTORS – TERM USED WHEN REFERRING TO BOTH MAGNITUDE AND DIRECTION EXAMPLES DISPLACEMENT = 30 KM EAST DISTANCE = 30 KM DIRECTION = EAST VELOCITY = 40 KM/HR WEST SPEED = 40 KM/HR DIRECTION = WEST

VECTOR OR SCALAR A RACECAR MOVING AT 110 MPH? A TURTLE STROLLING AT 200 CM/MIN? AN SUV MOVING AT 40 KM/HR EAST?

A SYSTEM MUST HAVE A ZERO POINT OR ORIGIN POSITION POSITION – DEFINED AS SOME LOCATION ON A COORDINATE SYSTEM 1-DIMENSION = A SINGLE NUMBER LINE (X COORDINATE) 2-DIMENSION = CARTESIAN COORDINATE PLANE (X,Y) 3-DIMENSION = 3D COORDINATE (X,Y,Z) HUMAN EXISTANCE = 4D COORDINATE (X,Y,Z,TIME) A SYSTEM MUST HAVE A ZERO POINT OR ORIGIN

1 – DIMENSIONAL MOTION ALONG A STRAIGHT LINE (# LINE) MUST HAVE A DESIGNATED ZERO POINT OR ORIGIN NEGATIVE VALUES TO THE LEFT (OR DOWN) POSITIVE VALUES TO THE RIGHT (OR UP)

DISTANCE & DISPLACEMENT SCALAR QUANTITY GIVING THE POSITIVE LENGTH BETWEEN TWO POINTS WE CAN DETERMINE DISTANCE TRAVELLED USING THE EQUATION: *X = IP1-P2I + IP2-P3I +… DISPLACEMENT THE DIFFERENCE BETWEEN THE FINAL AND INITIAL POSITIONS WE CAN FIND DISPLACEMENT USING THE EQUATION: *Δx = Pf – Pi, where Pf is the final position of the object and Pi is the initial position of the object.

SPEED VS VELOCITY

AVERAGE VS INSTANTANEOUS SPEED AVERAGE SPEED: TOTAL DISTANCE TRAVELED DIVIDED BY TOTAL TRAVEL TIME DISTANCE RECORDED ON A VEHICLE’S ODOMETER DIVIDED BY TOTAL TRAVEL TIME INSTANTANEOUS SPEED: THE SPEED OF AN OBJECT AT A PARTICULAR MOMENT(INSTANT) IN TIME READING ON YOUR SPEEDOMETER AT ANY GIVEN MOMENT SPEED LIKE DISTANCE IS A SCALAR QUANTITY AND THUS ALWAYS POSITIVE SPEED LIKE DISTANCE PROVIDES NO INFORMATION ABOUT DIRECTION

FORMULA: * V = (PF – PI)/(TF-TI) AVERAGE VELOCITY VELOCITY IS DIFFERENT THAN SPEED BECAUSE IT IS A VECTOR QUANTITY AND AS SUCH WILL HAVE BOTH MAGNITUDE AND DIRECTION. VELOCITY IS THE COMBINATION OF SPEED AND DIRECTION DEFINITION OF VELOCITY: CHANGE IN POSITION DIVIDED BY CHANGE IN TIME CHANGE OF POSITION CAN BE EITHER POSITIVE OR NEGATIVE, SO VELOCITY CAN BE POSITIVE OR NEGATIVE. FORMULA: * V = (PF – PI)/(TF-TI)

CALCULATE THE AVERAGE VELOCITY DETERMINING AVERAGE VELOCITY IF THE MOTION IS ALWAYS IN THE SAME DIRECTION, THE AVERAGE VELOCITY WILL HAVE THE SAME NUMERICAL VALUE AS THE AVERAGE SPEED, EXCEPT THAT A DIRECTION OF MOTION MUST ALSO BE GIVEN. IF MOTION CHANGES DIRECTION, THE AVERAGE VELOCITY WILL BE DIFFERENT THAN THE AVERAGE SPEED. AVERAGE VELOCITY DEPENDS ON THE TOTAL DISPLACEMENT AND TOTAL ELAPSED TIME DISPLACEMENT = PF – PI CAN BE POSITIVE – POSITIVE AVERAGE VELOCITY CAN BE NEGATIVE – NEGATIVE AVERAGE VELOCITY CAN BE ZERO – AVERAGE VELOCITY = ZERO

AVERAGE VS INSTANTANEOUS VELOCITY INSTANTANEOUS VELOCITY REFERS TO VELOCITY AT A SPECIFIC TIME, SUCH AS T=3.5 SECONDS. IT IS LIKE THE READIN OF A SPEEDOMETER COMBINED WITH A POINT FOR CURRENT DIRECTION. IN PRACTICE, WE CANNOT FIND A TRULY INSTANTANEOUS VELOCITY. INSTEAD, WE FIND AN AVERAGE VELOCITY OVER SMALLER INTERVALS OF TIME (ΔT). HOW A SPEEDOMETER WORKS *SPEED = CIRCUMFERENCE OF TIRE/TIME TO COMPLETE A SINGLE ROTATION. IN GENERAL, THE SLOPE OF THE LINE TANGENT TO A ‘POSITION-TIME’ CURVE ON A GRAPH GIVES THE INSTANTANEOUS VELOCITY.

DESCRIBING THE MOTION OF AN OBJECT GRAPHING HELPS GIVE US INSIGHT INTO HOW AN OBJECT MAY OR MAY NOT BE MOVING EXAMPLE 1 – MR. JONES EXAMPLE 2 – TWO CYCLISTS GRAPHING TOGETHER AS A CLASS.