IF WE MEASURE DISTANCE AND TIME, WE GET:

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Presentation transcript:

IF WE MEASURE DISTANCE AND TIME, WE GET: 1 2 3 4 10 20 30 40 FIRST, LET’S EXAMINE A CAR MOVING AT CONSTANT VELOCITY. IN THIS CASE, 10 m/s. IF WE MEASURE DISTANCE AND TIME, WE GET: Time, s 1 2 3 4 Dist., m 10 20 30 40

PLOTTING THE DATA ON A DISTANCE VS TIME GRAPH, WE GET THE FOLLOWING: THE SLOPE OF A P-T (D-T) GRAPH IS A STRAIGHT LINE, AND THE SLOPE IS VELOCITY (SPEED).

WHAT IS THE DIFFERENCE BETWEEN THE TWO GRAPHS BELOW? Graph 1 Graph 2

WHAT IS THE DIFFERENCE BETWEEN THE TWO GRAPHS BELOW? Graph 1 Graph 2 THE VELOCITY IS CONSTANT IN BOTH GRAPH. THE VELOCITY (SPEED) IS LESS IN GRAPH 1. IN GRAPH 2, THE OBJECT IS GOING FASTER THAN IN GRAPH 1.

WHAT IS THE DIFFERENCE BETWEEN THE TWO GRAPHS BELOW? Graph 3 Graph 4

WHAT IS THE DIFFERENCE BETWEEN THE TWO GRAPHS BELOW? Graph 3 Graph 4 OBJECTS IN BOTH GRAPHS HAVE NEGATIVE VELOCITY. THE OBJECT ON THE LEFT HAS A GREATER NEGATIVE VELOCITY.

SO, ON P-T (D-T) GRAPH, IF WE HAVE A STRAIGHT LINE, THE VELOCITY (SPEED) IS CONSTANT. IF THE SLOPE IS POSITIVE, THE VELOCITY (SPEED) IS POSITIVE. IF THE SLOPE IS NEGATIVE, THE VELOCITY IS NEGATIVE. WHAT IS GOING ON IF THE SLOPE IS 0?

NOW, LET’S SEE WHAT HAPPENS IF THE VELOCITY IS CHANGING. IN THIS CASE, THE VELOCITY IS CHANGING IN A POSITIVE DIRECTION TO THE RIGHT. Time, s 1 2 3 4 Dist., m 8 18 32

PLOTTING THIS DATA ON A P-T GRAPH GIVES US: IF THE SLOPE IS CONSTANT, THE VELOCITY IS CONSTANT. IF THE SLOPE IS CHANGING, THE VELOCITY IS CHANGING.

A CHANGE IN VELOCITY IS ACCELERATION. IF YOU ARE RIDING IN A CAR, AND THE CHANGE IN VELOCITY IS ENOUGH, YOU CAN SENSE IT. IF THE CAR GOES AROUND A CURVE, IF IT SLOWS DOWN, OR IF IT SPEEDS UP. ACCELERATION OCCURS IF: A CHANGE IN SPEED OCCURS A CHANGE IN DIRECTION OCCURS BOTH AVERAGE ACCELERATION IS THE TIME RATE OF CHANGE IN VELOCITY.

AVERAGE ACCELERATION = CHANGE IN VELOCITY/TIME FOR CHANGE TO OCCUR = a = Dv/Dt = (vf – vo)/t HERE, vo = velocity at time 0 vf = velocity at final time SINCE THE UNITS FOR VELOCITY ARE m/s THE UNITS FOR ACCELERATION ARE m/s2

AN OBJECT FALLING UNDER THE FORCE OF GRAVITY UNDERGOES AN ACCELERATION OF 9.8 m/s/s, ASSUMING NO AIR RESISTANCE.

IF VELOCITY AND ACCELERATION ARE BOTH IN THE SAME DIRECTION, THE OBJECT WILL SPEED UP – VELOCITY INCREASES. IF VELOCITY AND ACCELERATION ARE IN OPPOSITE DIRECTIONS, THE OBJECT WILL SLOW DOWN – VELOCITY DECREASES. GETTING BACK TO GRAVITY – IF THERE IS NO AIR RESISTANCE, DIFFERENT OBJECTS WILL FALL AT THE SAME RATE. d = distance = ½ gt2

WHAT IS HAPPENING IN BOTH CASES BELOW?

WHAT IS HAPPENING IN BOTH CASES BELOW? IN BOTH CASES, THE VELOCITIES ARE CHANGING FROM SLOW TO FAST. A HAS A POSITIVE VELOCITY, AND B HAS A NEGATIVE VELOCITY.

YOU CAN ALSO USE V-T (VELOCITY VERSUS TIME) GRAPHS TO ANALYZE MOTION YOU CAN ALSO USE V-T (VELOCITY VERSUS TIME) GRAPHS TO ANALYZE MOTION. CONSIDER THE FOLLOWING SITUATION: Time, s Dist., m 1 10 2 20 3 30 4 40

THE SLOPE OF A V-T GRAPH IS ACCELERATION. Time, s V, m/s 1 10 2 20 3 30 4 40

IF THE SLOPE OF A V-T DIAGRAM IS A STRAIGHT LINE, ACCELERATION IS CONSTANT. WHAT IS HAPPENING IN THE FOLLOWING SITUATION?

WHAT IS HAPPENING BELOW:

WHAT IS HAPPENING BELOW: A IS AT CONST. VELOCITY. B IS DECELERATING. C IS AT CONST. VELOCITY, BUT LOWER THAN IN A.

WHAT IS HAPPENING BELOW:

WHAT IS HAPPENING BELOW: A IS SLOWING DOWN. B IS STOPPED. C HAS NEGATIVE VELOCITY AND IS ACCELERATING IN A NEGATIVE DIRECTION.

WHAT HAPPENS BELOW:

WHAT HAPPENS BELOW: DURING INTERVAL A, IT IS MOVING AT CONSTANT VELOCITY. DURING INTERVAL B, IT SLOWS DOWN AND STOPS. DURING INTERVAL C, IN MOVES IN THE NEGATIVE DIRECTION AND SPEEDS UP.