1. Understanding Motion Linear Motion

2. Motion The motion of an object can only be recognized when something is established as a basis of comparison…a reference point We say an object is moving when its position changes compared to that reference point For most day-to-day situations, the Earth, and those things affixed to it, serve as a convenient reference frame.

3. Position and Time These are the two most fundamental physical quantities that can be measured to describe an object’s motion. The relationship between these variables can be discovered experimentally and modeled using mathematics in both graphical and equation form.

4. Position vs. Time Graphs The magnitude (size) of the slope tells us… The algebraic sign of the slope tells us… The magnitude and sign together tell us… The vertical intercept tells us… When this graph is a straight line we know…

5. Position vs. Time Graphs The generic equation for a linear graph is… y = mx + b In terms of the physical quantities being plotted this becomes… x = mt + b Time, t (s) Position, x (m)

6. Position vs. Time Graphs If we replace the slope and intercept terms with what they tell us we get… x = vt + x i Where v is the velocity (m/s) and x i is the initial position (m) of the object in motion Time, t (s) Position, x (m) xixi m = v

7. x = vt + x i This equation (straight line with slope v and intercept x i ) is a model that describes the relationship between position and time for an object moving with constant velocity. x = position of object after time, t v = velocity of object (speed in a direction) t = elapsed time x i = starting position of the object

8. Constantly Accelerated Motion (ball on a ramp) Position-time graphs are NOT linear, they are quadratic… x  t 2 – slope is NOT constant  Velocity is changing Velocity-time graphs are linear… v  t – Slope is constant  The rate at which velocity is changing is constant SLOPE = ACCELERATION

9. v = at + v o This equation is a model describing the relationship between velocity and time for an object that is constantly accelerating v – velocity after time, t a – acceleration t – elapsed time v o – starting velocity

10. x = ½ at 2 + v o t + x o This equation models the relationship between position and time for constantly accelerated motion This equation emerges from our ball on a ramp data or it could be derived (we will!) x = position after time, t a = acceleration v o = starting velocity t = elapsed time x o = starting position

11. Free Fall An object is considered to be in free fall when it is only under the influence of gravity Objects in free fall near the surface of Earth experience constant acceleration… a = g = 9.80 m/s 2 downwards

12. “Fall” is misleading An object can be in free fall while it is traveling upwards (only under the influence of g) – Slows down at a constant rate equal to the rate that a falling object gains speed

13. Free Fall Equations v avg =  x/t a =  v/t v = v o + at  x = v o t + ½ at 2 v 2 = v o 2 + 2a  x Nothing new here! Free fall is constantly accelerated motion so the kinematics equations are all applicable. Remember a = g = 9.80m/s 2 (downward) ***When problem solving, pay close attention to direction of quantities!!!! Often you will find x changed to y when working on vertical motion problems

14. Sample Problem A volley ball is hit straight upward with a speed of 6.0 m/s. If the volley ball starts 2.0 m above the floor, how long will it be in the air before hitting the floor?