9 Instantaneous Acceleration -- graph The slope of the velocity vs. time graph is the accelerationThe green line represents the instantaneous accelerationThe blue line is the average acceleration
10 Acceleration and Velocity, 1 When an object’s velocity and acceleration are in the same direction, the object is speeding upWhen an object’s velocity and acceleration are in the opposite direction, the object is slowing down
11 Example Acceleration and velocity are in opposite directions Acceleration is uniform (blue arrows maintain the same length)Velocity is decreasing (red arrows are getting shorter)Positive velocity and negative acceleration
16 Kinematic EquationsThe kinematic equations may be used to solve any problem involving one-dimensional motion with a constant accelerationYou may need to use two of the equations to solve one problemMany times there is more than one way to solve a problem
17 Kinematic Equations, specific For constant a,Can determine an object’s velocity at any time t when we know its initial velocity and its accelerationDoes not give any information about displacement
18 Kinematic Equations, specific For constant acceleration,The average velocity can be expressed as the arithmetic mean of the initial and final velocities
19 Kinematic Equations, specific For constant acceleration,Gives final position in terms of velocity and accelerationDoesn’t tell you about final velocity
20 Graphical Look at Motion – displacement – time curve The slope of the curve is the velocityThe curved line indicates the velocity is changingTherefore, there is an acceleration
21 Graphical Look at Motion – velocity – time curve The slope gives the accelerationThe straight line indicates a constant acceleration
22 Graphical Look at Motion – acceleration – time curve The zero slope indicates a constant acceleration
23 This is called free fall. Let’s get real and throw something out of a building and watch it fall.This is called free fall.
24 Freely Falling Objects A freely falling object is any object moving freely under the influence of gravity alone.It does not depend upon the initial motion of the objectDropped – released from restThrown downwardThrown upward
25 Acceleration of Freely Falling Object The acceleration of an object in free fall is directed downward, regardless of the initial motionThe magnitude of free fall acceleration is g = 9.80 m/s2g decreases with increasing altitudeg varies with latitude9.80 m/s2 is the average at the Earth’s surfaceIn the English/American system, g=32 ft/sec2.
26 Acceleration of Free Fall/Rise, cont. We will neglect air resistanceFree fall motion is constantly accelerated motion in one dimensionUse the kinematic equations to solve problems.
27 Free Fall Example Let’s drop an object from the top of this building by simply releasing it.How long will it take to get to the ground?How fast will it be going when it gets to theground?What color is the object?Issues –Where is the origin?IS y the same thing as x?? How can that be???