AP Physics B - Kinematics

1 KinematicsAP Physics BDefining the important variablesKinematicsis a way of describing the motion of objects without describing the causes. You can describe an object s motion:In wordsMathematicallyPictoriallyGraphicall yNo matter HOW we describe the motion, there are several KEY VARIABLES that we velocityvm/s/sAcceleration due to gravityg or agm/sInitial velocityvomDisplacementx or ym/s/sAccelerationasTimetUnitsVariableSy mbolThe 3 Kinematic equations There are 3 major kinematic equations than can be used to describe the motion in are used when the acceleration is CONSTANT.)(221222oooooxxavvattvxxatvv +=++=+=Kinematic #1atvvatvvtvvtvaooo+== =Kinematic #1 Example:A boat moves slowly out of a marina (so as to not leave a wake) with a speed of m/s. As soon as it passes the breakwater, leaving the marina, it throttles up and accelerates at m/ = 5 sa = m/s/sv = ?

2 Vo= m/sWhat do I want?What do I know?a) How fast is the boat moving after accelerating for 5 seconds?=+=+=vvatvvo)5)( () ( m/sKinematic #2221attvxxoxo++=b) How fardid the boat travel during that time?=++=++=xxattvxxoxo)5)( (21)5)( ( mDoes all this make sense? ) )(5(== =mAbhA30)12)(5(2121= = ) )(5(== =Total displacement = + 30 = m = Total AREA under the to Notevttvxxatttvxxattvxxoxooxooxo ++=++=++=2121212A = HBA=1/2 HBMost of the time, xo=0, but if it is not don t forget to ADD in the initial position of the object. Kinematic #3)(222ooxxavv +=V = 0 m/sa = m/s/sx = ?vo= 12 m/sWhat do I want?What do I know?Example:You are driving through town at 12 m/s when suddenly a ball rollsout in front of your car. You apply the brakes and begin decelerating at m/ far do you travel before coming to a complete stop?

3 = = += +=xxxxxavvoo7144)0)( (2120)( mCommon Problems Students HaveI don t know which equation to choose!!!tvxMissing VariableEquationatvvo+=221attvxxoxo++=)( 222ooxxavv += Kinematics for the VERTICAL DirectionAll 3 Kinematics can be used to analyze one dimensional motionin either the X direction OR the y direction.)(2)(22121222222ooyyooxoyooxoo yyoyygvvxxavvgttvyyattvxxgtvvatvv += +=++= ++=+= += g or ag The Acceleration due to gravityThe acceleration due to gravity is a special constant that exists in a VACUUM, meaning without air resistance. If an object is in FREE FALL, gravity will CHANGEan objects velocity by m/s every ==The acceleration due to gravity: ALWAYS ACTS DOWNWARD IS ALWAYS CONSTANT near the surface of EarthExamplesA stone is dropped at rest from the top of a cliff. It is observed to hit the ground s later.

4 How high is the cliff?yo=0 mt = sg = m/s2y = ?voy= 0 m/sWhat do I want?What do I know?Which variable is NOT given andNOT asked for?Final Velocity!221gttvyyoyo++== =yy2) ( ) )(0( mH = pitcher throws a fastball with a velocity of m/s. It is determined that during the windup and delivery the ball covers a displacement of meters. This is from the point behind the body when the ball is at rest to the point of release. Calculatethe acceleration during his throwing motion. v = m/sx = ma = ?vo= 0 m/sWhat do I want?What do I know?Which variable is NOT given andNOT asked for?TIME)(222ooxxavv +== +=aa) ( m/s/sExamplesHow long does it take a car at rest to cross a m intersection after the light turns green, if the acceleration of the car is a constant m/s/s?a = m/s/sx = 35 mt = ?

5 Vo= 0 m/sWhat do I want?What do I know?Which variable is NOT given andNOT asked for? Final Velocity=++=tt2)2(21)0(035221attvxxoxo++ = sExamplesA car accelerates from m/s to 25 m/s in seconds. What was the acceleration?t = 6sv = 25 m/sa = ?vo= m/sWhat do I want?What do I know?Which variable is NOT given andNOT asked for? DISPLACEMENT atvvo+==+=aa)6( m/s/s