Average Velocity for Constant Acceleration

<?xml version="1.0" encoding="UTF-8"?>  <XholonWorkbook> <Notes> Khan Academy ------------ Title: Average Velocity for Constant Acceleration Description: Calculating average velocity when acceleration is constant Url: http://www.khanacademy.org/video/average-velocity-for-constant-acceleration?playlist=Physics InternalName: average-velocity-for-constant-acceleration YoutubeId: MAS6mBRZZXA Keywords: distance, kinematics, average, acceleration, physics My Notes ======== some conventions for this exercise positive number means to the right, negative number means to the left one dimension Part A ------ vi = 5m/s a = 2m/s^2 delta t = 4s a graph with time and velocity axes slope of the velocity line is a constant acceleration vf after 4 s 5m/s + delta t * a = 5m/s + 4s * 2m/s = 13m/s Part B ------ What is the total distance we have traveled? 5:50 the area under the curve on the graph break the irregularly-shaped area down into 2 different areas 1. rectangular area = 4s * 5m/s = 20m how far traveled if not accelerating 2. triangular area = 0.5 * 4s * (vf - vi) = 0.5 * 4 * 8 = 16m how much further because we are accelerating so the total displacement is 20 + 16 = 36m distance = delta t * ((0.5 * vi) + (0.5 * vf)) average velocity = 0.5 * (vi + vf) this works because the acceleration is constant distance = delta t * average velocity </Notes> <script implName="lang:python:inline:"><![CDATA[ # Part A: final velocity a = 2 # m/s^2 vi = 5 # m/s dt = 4 # s vf = vi + dt * a print "Final velocity = " + str(vf) # result: Final velocity = 13 # # Part B: total displacement averageVelocity = 0.5 * (vi + vf) displacement = dt * averageVelocity print "Displacement = " + str(displacement) # result: Displacement = 36.0 #http://ideone.com/Ns8sJ ]]></script> <script implName="lang:javascript:inline:"><![CDATA[ // Part A: final velocity var a = 2; // m/s^2 var vi = 5; // m/s var dt = 4; // s var vf = vi + dt * a; // Part B: total displacement var averageVelocity = 0.5 * (vi + vf); var displacement = dt * averageVelocity; println("Final velocity = " + vf + ", Displacement = " + displacement); //javascript:(function(a,vi,dt){var vf=vi+dt*a;var averageVelocity=0.5*(vi+vf);var displacement=dt*averageVelocity;alert("Final velocity = "+vf+", Displacement = "+displacement);})(2,5,4) // result: Final velocity = 13, Displacement = 36 ]]></script> <_-.XholonClass>  <PhysicalSystem/> <Block/>  <Height superClass="Length"/> </_-.XholonClass> <xholonClassDetails> <Block> <port name="height" connector="#xpointer(Height)"/> </Block> </xholonClassDetails> <PhysicalSystem> <Block> <Height>0.1 m</Height> </Block> </PhysicalSystem> <Blockbehavior implName="lang:python:inline:"><![CDATA[ # This works if pasted in as a last child of Block. height.incVal(0.02) print("Python wants something to do. Height:" + str(height)) ]]></Blockbehavior> <Blockbehavior implName="lang:javascript:inline:"><![CDATA[ // This works if pasted in as a last child of Block. height.incVal(0.02); print("JavaScript wants something to do. Height:" + height + "\n"); ]]></Blockbehavior> <Blockbehavior implName="lang:bsh:inline:"><![CDATA[ // This works if pasted in as a last child of Block. height.incVal(0.02); System.out.print("Java/Beanshell wants something to do. Height:" + height + "\n"); ]]></Blockbehavior> <Blockbehavior implName="lang:jruby:inline:"><![CDATA[ require 'java' # This works if pasted in as a last child of Block. $height.incVal(0.02) puts "Ruby wants something to do. Height: #{$height}" ]]></Blockbehavior> <Blockbehavior implName="lang:groovy:inline:"><![CDATA[ // This works if pasted in as a last child of Block. height.incVal(0.02); System.out.print("Groovy wants something to do. Height:" + height + "\n"); ]]></Blockbehavior> </XholonWorkbook>