x i = x * means change in so x = change in x Speed and Velocity distance travelled speed= elapsed time average velocity v av

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1 Motion in 1 Dimension Kinematics: the study of motion Position, Distance and Displacement Needed: 1 coordinate system ( position is relative ) often chosen with a convenient origin Distance = total length of travel vs. Displacement = change in position = final position - initial position = x f x i Example Consider various trips and the corresponding distances/displacments = x * FH YH RWM 2.1mi 4.3mi means change in so x = change in x Phys297P2:1 Speed and Velocity distance travelled speed= elapsed time average velocity v av = x velocity v=rate of change of displacement =slope of displacement vstime graph x =lim t 0 tangent and tangents animations displacement time x note:average velocity equals instantaneous velocity if velocity is constant Motion Sensor Demo Phys297P2:2

2 acceleration: rate of change of velocity changes in speed as well as direction of travel average velocity: the ratio of the displacement during a time interval to the length if the time interval a av =average acceleration= v 2 v 1 = v t 2 t 1 t Graphical Interpretation of acceleration Acceleration is the slope of the graph of velocity versus time may be positive or negative (direction!) Instantaneous Acceleration is the slope velocity time v Acceleration is the concavity of the graph of position versus time average acceleration equals instantaneous acceleration if acceleration is constant instantaneous acceleration = slope of velocity versus-time graph Phys297P2:3 The rate of change of acceleration is the Jerk Not useful unless acceleration is changing quickly (Rides!!!!) A mechanical shock is a pulse of acceleration G-force Sitting at rest, one feels one g due to gravity The acceleration of gravity is 9.81 m/s 2 (about 10 m/s 2 ) G-force = number of g's of acceleration Phys297P2:4

3 Physiological affects of acceleration depends upon direction of G-force (horizontal vs. vertical) short vs. long duration (and the Jerk) examples pooling of blood away from the brain permanent retinal damage limits for vertical 5 g's till blackout (9 g's for professional pilot) -2 to -3 g's till redout limits for horizontal 17 9's eyeballs in, 12 g's eyeballs out Death or serious injury likely at 50 g's Phys297P2:5 Activity : Graphical Exploration of Motion and Moving-Man Phys297P2:6

4 Motion with Constant Acceleration constant acceleration slope of velocity-time graph is straight line v = v 0 +at average velocity: v av = x = x 0 t 0 v av = v+v 0 2 w/ substitution and some algebra v v 0 t x= v+v 0 t 2 and v 2 =v a x The Fab Four x= 1 2 (v 0 +v)t x=v 0 t+ 1 2 a t 2 v=v 0 +a t v 2 =v a x Phys297P2:7 Problem Solving Tips Draw a diagram Write down all known quantities, identify on diagram. Write down all unknown quantities, identify on diagram. Find basic equation which relates each unknown quantity to known quantities. Solve equation for the desired unknown. plug and chug Phys297P2:8

5 Example: A dragster accelerates at the rate of 7.40 m/s 2. How far is it from its starting point after 1.0s? How fast is it going after 3.0s? How fast is it going at these times? Example: A driver cruising at 11.4 m/s spots a deer in his headlights and immediately hits his brakes, slowing with a deceleration of 3.80 m/s 2. If the deer is 20.0 m from the car when the brakes are applied, how close is the dear to being hit? How much time does it take the car to come to a rest? Phys297P2:9 Acceleration of Gravity, A Model Historical Perspective: Attempts to describe motion by Galileo Experiment and observation as the foundation of science ramps and free fall idealizations and simplifications: ignoring air resistance g = 9.81 m/s 2 (9.78 at equator, 9.83 at poles) = 32 ft/s 2 a = g, acceleration is directed downwards (watch directions in problems!!!) usually take up positive, so a = 9.81 m/s 2 Phys297P2:10

6 Example: A penny is dropped from the top of the Empire State Building (height: 381 m= 1,250 ft). Neglecting air resistance, how fast is the penny moving when it hits the ground? Example: Penny is dropped from the top of the Empire State Building (height: 381 m=1,250 ft). Superman catches her at a height of 10.0 m above the ground and brings her to rest at ground level. What was her acceleration during that last 10.0 m? Phys297P2:11 Free Fall Video Analysis zoom to fit set calibration stick (ruler) = 1 m create point mass shift click points only for frames where the object is in free fall Select y for vertical axis Analyze Data (right click on graph and select analyze) Curve fit (at^2+bt+c and fab four > g = 2 a ) One Data Tool Printout per group, comments hand written on back. (Don't forget your names!) Phys297P2:12

7 Going for a ride: Elevator Ride applet Phys297P2:13