PHYSICS ONEDIMENSIONAL MOTION DISPLACEMENT AND VELOCITY ONEDIMENTIONAL MOTION

PHYSICS ONE-DIMENSIONAL MOTION: DISPLACEMENT AND VELOCITY

ONE-DIMENTIONAL MOTION TAKES PLACE IN A SINGLE DIRECTION. EX: TRAIN MOVING ON A STRIGHT SET OF TRACKS, ABLE TO MOVE FORWARD AND BACKWARDS, BUT NOT LEFT AND RIGHT (OR UP AND DOWN).

MOTION TAKES PLACE OVER TIME AND DEPENDS UPON THE FRAME OF REFERENCE=A COORDINATE SYSTEM FOR SPECIFYING THE PRECISE LOCATION OF OBJECTS IN SPACE (LETS YOU MEASURE CHANGES IN POSTION). I. E: SO IF AN OBJECT IS AT REST, ITS POSTION DOES NOT CHANGE WITH RESPECT TO ITS FRAME OF REFERENCE.

DISPLACEMENT = CHANGE IN POSITION OF AN OBJECT. SO: ANY OBJECT THAT MOVES FROM ONE POSTION TO ANOTHER, THE LENGTH OF THE STRIGHT LINE DRAWN FROM ITS INITIAL POSTION TO THE OBJECTS FINAL POSTION IS CALLED THE DISPLACEMENT OF THE OBJECT.

DISPLACEMENT FORMULA ∆x=xf-xi DISPLACEMENT=(CHANGE IN POSTION=FINAL POSTION–INITIAL POSTION) *REMEMBER THE GREEK LETTER DELTA (∆) BEFORE THE x DENOTES A CHANGE IN THE POSTION OF THE OBJECT.

� EX: A CAR DRIVES FROM POINT A TO POSTION B 64 km AWAY WHAT IS THE DISPLACEMENT OF THE CAR? � SO USING: ∆x=xf-xi ∆x=64 km - 0 km SO: ∆x=64 km • * DISPLACEMENT IS NOT ALWAYS EQUAL TO THE DISTANCE TRAVELED (WHAT IF THE CAR TRAVALED BACKWARDS) • * DISPLACEMENT CAN BE POSITIVE OR NEGATIVE, DEPENDING ON THE DIRECTION.

EX 1: ∆x=8 cm-1 cm ∆x=7 cm • EX 2: ∆x=2 cm-10 cm ∆x=-8 cm

VELOCITY �TELLS US HOW FAST AND IN WHICH DIRECTION AN OBJECT IS MOVING. �AVERAGE VELOCITY =THE TOTAL DISPLACEMENT DIVIDED BY THE TIME INTERVAL DURING WHICH THE DISPLACEMENT OCCURRED. �THE SI OR METRIC UNIT OF VELOCITY IS METERS PER SECOND (m/s).

AVERAGE VELOCITY FORMULA OR

EX: YOU TAKE A ROAD TRIP TO A FRIENDS HOUSE 370 km TO THE WEST ALONG A STRIGHT LINE, IF YOU LEFT THE HOUSE AT 10: 00 A. M. AND ARRIVED AT YOUR FRIENDS HOUSE AT 3: 00 P. M. , YOUR AVG VELOCITY WOULD BE? WEST 0 km EAST -370 km TIME TAKEN 10: 00 AM-3: 00 PM= 5 hr

THIS VALUE IS AN AVERAGE!! YOU PROBABLY DID NOT TRAVEL EXACTLY 74 (km/hr) AT EVERY MOMENT. (YOU MAY HAVE STOPPED FOR SOME REASON) AVG VELOCITY = TO THE CONSTANT VELOCITY NEEDED TO COVER THE GIVIN DISPLACEMENT IN A GIVIN TIME INTERVAL.

EX 1: DURING A RACE, ANDRA RUNS WITH AN AVG VELOCITY OF 6. 02 m/s TO THE EAST. WHAT DISTANCE DOES ANDRA COVER IN 137 s? GIVIN: vavg=6. 02 m/s ∆t= 137 s UNKNOWN: ∆x=? *REARRANGE THE AVG VELOCITY EQUATION TO SOLVE FOR DISPLACEMENT. * TOO SOLVE: ∆x=vavg∆t=(6. 02 m/s)(137 s)=825 m to the east

EXTRA NOTES ON VELOCITY IS NOT THE SAME AS SPEED. (VELOCITY HAS BOTH MOTION AND DIRECTION. ) (SPEED HAS NO DIRECTION ONLY MOTION. ) VELOCITY CAN BE INTERPRETED GRAPHICALLY. VELOCITY OF AN OBJECT CAN BE DETURMINED IF ITS POSTION IS KNOWN AT SPECIFIC TIMES ALONG ITS PATH. (USE A GRAPH)

Motion of an object moving with constant velocity OBJECT 1 WHAT TYPE OF VELOCITY IS THIS GRAPH SHOWING FOR OBJECT 1, 2, & 3? POSITION + VELOCITY AT REST - VELOCITY TIME OBJECT 2 OBJECT 3

INSTANTANEOUS VELOCITY THE VELOCITY OF AN OBJECT AT SOME INSTANT (OR SPECIFIC POINT IN ITS PATH). ONE WAY TO DETERMINE THE INSTANTANEOUS VELOCITY IS TO CONSTRUCT A STRAIGHT LINE THAT IS TANGENT TO THE POSTION VS TIME GRAPH AT THAT INSTANT. THE SLOPE OF THIS TANGENT LINE IS EQUAL TO THE VALUE OF THE INSTANTANEOUS VELOCITY AT THAT POINT.

INSTANTANEOUS VELOCITY MAY NOT BE THE SAME AS AVG VELOCITY. CONSIDER AN OBJECT WHOSE POSTION VS TIME GRAPH IS NOT A STRAIGHT LINE, BUT A CURVE. THE OBJECT MOVES THROUGH LARGER AND LARGER DISPLACEMENTS AS EACH SECOND PASSES: THUS VELOCITY INCREASES WITH TIME. THRUGH EACH TIME INTERVAL WE ARE INCREASING VELOCITY

EX: BETWEEN t=0 s AND t=20 s, THE OBJECT MOVES 8. 0 m, AND ITS AVG VELOCITY IN THIS TIME INTERVAL IS 4. 0 m/s. HOWEVER , BETWEEN t=0 s AND t=4. 0 s, IT MOVES 32 m, SO ITS AVG VELOCITY IN THIS TIME INTERVAL IS 8. 0 m/s. WE OBTAIN DIFFERENT AVG VELOCITIES, DEPENDING ON THE TIME INTERVAL WE CHOOSE. But how can we find the velocity at an instant of time? USING INSTANTANEOUS VELOCITY

EX: WHAT IS THE INSTANTANEOUS VELOCITY between(t=5 s and t=6 s) Xf=15 m v=5 m/s TANGENT LINE tf=6 s xi=10 m ti=5 s SO: INSTANTANEOUS VELOCITY WOULD v= 5 m/s

PRACTICE PROBLEMS The peregrine falcon is the fastest of flying birds (and, as a matter of fact, is the fastest living creature). A falcon can fly 1. 73 km downward in 25 s. What is the average velocity of a peregrine falcon? Bonnie Blair set the world record for women’s speed skating in 1995, with an average speed of 12. 9 m/s. How far would Blair have traveled at this speed in a time of 5. 00 minutes?