1. Advanced Physics Chapter 2 Describing Motion: Kinematics in One Dimension

2. Chapter 2  2.1 Reference Frames and Displacement  2.2 Average Velocity  2.3 Instantaneous Velocity  2.4 Acceleration  2.5 Motion at Constant Acceleration  2.6 Solving Problems  2.7 Falling Objects  2.8 Graphical Analysis of Linear Motion

3. Describing Motion Mechanics  Study of the motion of objects and the related concepts of force and energy Kinematics  Description of how objects move Dynamics  Deals with force and why objects move as they do Translational Motion  Objects that move without rotating

4. 2.1 Reference Frames and Displacement  All measurements (position, distance, speed) must be made relative to a frame of reference.  A set of coordinate axes are drawn to represent a frame of reference.  Usually the origin is considered the reference point of all measurements.

5. 2.1 Reference Frames and Displacement  An object’s position (x) is where it is relative to a specified reference point. It can be represented by the coordinates on a set of coordinate axes in a reference frame.

6. 2.1 Reference Frames and Displacement Distance  the total path an object moves.  Scalar quantity Displacement  the change in position of an object.  It is the distance between the starting and ending position of an object.  Vector quantity (positive or negative)   x = x 2 – x 1

7. 2.2 Average Velocity Speed  How far an object travels in a given time interval (huh?)  The rate of change of an object’s motion  Average speed = Distance traveled/time elapsed  Scalar

8. 2.2 Average Velocity Velocity  Difference in position of an object in a given time interval (huh?)  Rate of change of an object’s position  Average velocity = displacement/time elapsed  v =  x/  t = (x 2 – x 1 )/(t 2 – t 1 )  Vector (positive or negative)

9. 2.3 Instantaneous Velocity Instantaneous Velocity  The velocity of an object in any instant  The average velocity of an object over an infinitesimally short time interval  v = lim  x/  t  t 0  Instantaneous velocity and instantaneous speed are always equal (?)

10. 2.4 Acceleration Average acceleration  The change in an object’s velocity divided by the time it takes to make this change  The rate of change of an object’s velocity  a =  v/  t = (v 2 – v 1 )/(t 2 – t 1 )  Vector quantity (2 positive and 2 negative)

11. 2.4 Acceleration Instantaneous acceleration  The acceleration of an object in any instant  The average acceleration of an object over an infinitesimally short time interval  a = lim  v/  t  t 0

12. 2.5 Motion at Constant Acceleration  x = x o + vt  v = v o + at  v = (v o + v)/2  x = x 0 + v o t + 1/2at 2  v 2 = v o 2 + 2a(x – x o )

13. 2.6 Solving Problems 1. Read and reread the whole problem carefully. 2. Draw a diagram of the situation. 3. Write down knowns and unknowns. 4. Select the proper equation to solve problem (has knowns and unknowns). 5. Put knows into equation (check units!) and solve. 6. Check your answer (reasonable?) and write down correct units

14. 2.6 Solving Problems Homework problems  p.43; 19-24

15. 2.7 Falling Objects  All objects fall with the same constant acceleration in the absence of air resistance or other resistance.  Object with different masses will change speed at the same rate regardless of their masses.  Galileo—father of modern science  At a given location on the Earth and in the absence of air resistance, all objects fall with the same constant acceleration

16. 2.7 Falling Objects Acceleration due to gravity (g)  g = – 9.80 m/s 2  An object is always accelerated down by gravity  Falling object speeds up, upward moving object slow down

17. 2.7 Falling Objects A ball is thrown up with an initial velocity of 15 m/s.  What is the ball’s velocity when it returns to the thrower’s hand  How high does the ball go?  What is its velocity at the top of its path?  How long does it take to get to the top of its path?  How long is the ball in the air?  At what time does the ball pass a point 8 m above the thrower’s head? (quadratic equation?)

18. 2.7 Falling Objects A ball is thrown up with an initial velocity of 15 m/s.  What is the ball’s velocity when it returns to the thrower’s hand? –15 m/s  How high does the ball go? 11.5 m  What is its velocity at the tope of its path? 0 m/s  How long does it take to get to the top of its path? 1.53 s  How long is the ball in the air? 3.06 s  At what time does the ball pass a point 8 m above the thrower’s head? (quadratic equation?) 0.69 s & 2.37 s (why?)

19. 2.8 Graphical Analysis of Linear Motion GraphPointsSlopeArea P—TPositionVelocityCrap V—TVelocityAccelerationDisplacement A—TAccelerationGarbageVelocity

20. 2.8 Graphical Analysis of Linear Motion Slope Slope of a straight line  Change in the dependent variable (  y) divided by the change in the independent variable (  x)  Slope = rise/run =  y/  x Slope of a point on a curved line  Slope of the tangent to the curve at that point  Instantaneous vs. average