2. MOTION IN ONE DIMENSION AVERAGE / INSTANTANEOUS SPEED POSITION AND DISPLACEMENT AVERAGE / INSTANTANEOUS VELOCITY AVERAGE / INSTANTANEOUS ACCELERATION MOTION WITH CONSTANT ACCELERATION FREE FALL P P P P P P

3. KINEMATICS is the study of motion in time and space without considering the cause of the motion. P POSITION is the location of an object with reference to a coordinate system. In one dimension the coordinatex is usually used. P When an object is stationary (at rest) its position does not change. When an object is moving its position does change. P During a specific time interval in which motion occurs the object moves from an initial positionx i at the beginning of the time interval to a final positionx f at the end of the time interval. P The beginning and end of the time interval are designated t i (initial) andt f (final) respectively.

4. DISPLACEMENT is the change in position of an object. Displacement is designated  x. A VECTOR is a physical quantity that has both size (magnitude) and direction. Physical quantities that do not have direction are SCALARS. Position and displacement are both vectors. For vectors in one dimension, there are only two directions; toward + 4 or toward - 4. If the vector points toward + 4, the vector is positive, like +6m. If the vector points toward - 4, the vector is negative, like -6m. Thus the + and - signs are used to designate direction for one dimensional vectors.

5. If the wheel moves from x = -1 to x = 3 and then to x = -2, what overall displacement has the wheel experienced? -4-3 -2 0 12 34 Start ReverseFinish EXAMPLE:

6. If the wheel moves from x = -1 to x = 3 and then to x = -2, what overall displacement has the wheel experienced? -4-3 -2 0 12 34 Start ReverseFinish ANSWER

7. Average velocity is designated and is defined as displacement,  x, divided by the time over which the displacement occurs,  t. v How is average velocity different from average speed? Average speed is the total distance traveled divided by the total travel time. Since distance is always positive and has no direction, average speed also is always positive and has no direction. Average velocity does depend on direction and may be positive or negative depending on direction. Usually an object’s average speed isn’t numerically equal to its average velocity. Do not use the word speed when you mean velocity.

9. The INSTANTANEOUS VELOCITY, designated v, of a moving object is its velocity determined at an instant in time. The instantaneous speed of an object is the magnitude of its instantaneous velocity. No other relationship between speed and velocity exists.

10. t x Red curve shows a plot of position vs time for an object in motion Slope of tangent line equals the instantaneous velocity of the object at that point on the graph.  x  t

11. If the wheel moves from x = -1m at t = 0 to x = 4m at t = 3s, and then to x = -3m at t = 8s, what are the overall average speed and average velocity of the wheel? -4-3 -2 0 12 34 Start ReverseFinish EXAMPLE:

12. If the wheel moves from x = -1m at t = 0 to x = 4m at t = 3s, and then to x = -3m at t = 8s, what are the overall average speed and average velocity of the wheel? -4-3 -2 0 12 34 Start ReverseFinish ANSWER

13. The AVERAGE ACCELERATION of an object in motion,, is its change in velocity divided by the time it takes for the change to occur. a Effects of Acceleration: P When an object’s velocity and acceleration are in the same direction, the object speeds up. P When velocity and acceleration are in opposite directions, the object slows down. P When an object changes its direction of motion, only its velocity vector changes direction (or sign). At the position of the change in direction, velocity is instantaneously zero but acceleration is non-zero.

15. INSTANTANEOUS ACCELERATION is the acceleration an object has at a certain time, for an instant. It is defined as: Displacement is change in position. Velocity is the rate of change in position. Acceleration is the rate of change in velocity.

16. Red curve is graph of instantaneous velocity vs time for an object in motion v t  v  t Slope of tangent line is the instantaneous acceleration occurring at that point.

21. EXAMPLE:While being thrown a baseball moves from rest to a speed of about 90 mph in distance about that of 1.5m. Calculate the acceleration of such a baseball.

22. ANSWER:While being thrown a baseball moves from rest to a speed of about 90 mph in distance about that of 1.5m. Calculate the acceleration of such a baseball.

26. EXAMPLE: A ball is thrown vertically upward near the edge of the roof of a tall building 60m above the ground. The initial upward speed of the ball is 12m/s. On the way down, the ball will just miss the edge of the building. (a) What maximum height does the ball reach? (b) How long is the ball in the air? (c) What is the speed of the ball when it strikes the ground?

27. ANSWER: A ball is thrown vertically upward near the edge of the roof of a tall building 60m above the ground. The initial upward speed of the ball is 12m/s. On the way down, the ball will just miss the edge of the building. (a) What maximum height does the ball reach? (b) How long is the ball in the air? (c) What is the speed of the ball when it strikes the ground?