Acceleration© Copyright NewPath Learning. All Rights Reserved. 94-4881Visit www.newpathlearning.com for Online Learning Resources.Acceleration is the rate at which an object’s velocity changes. A change in velocity can be an increase or decrease in speed, or a change in direction. A race car accelerates, gaining speed, when it starts a race. The car decelerates, or has negative acceleration, when it slows down and stops to re-fuel. A race car traveling around the track at a constant speed also has acceleration because it is changing direction.acceleration = rate of change in velocityCalculating AccelerationIf an object is changing speed, but not changing direction, you can calculate acceleration. Basically, acceleration equals the change of speed of an object, . Imagine a roller coaster car at the peak of a steep drop. The initial speed of the car is 0 m/sec, and its speed at the bottom of the peak is 30 m/sec. It takes three seconds to travel from the top to the bottom. The roller coaster accelerated at 10 m/sec2.10152025303540455055acceleration = change of speedtimeinitial speed 0 m/sec30 m/secacceleration = 30 m/s3 sec= 10 m/sec2Distance vs. Time GraphAccelerationdistance vs. time graph. The slope of the line represents an object’s speed. A straight line indicates no change in speed, therefore the object is not accelerating. A indicates that the object’s speed is changing. A curve with a slope that’s getting steeper, tells us that the object is accelerating. A line curved in the opposite direction indicates that the object is decelerating.Speed vs. Time GraphThe acceleration of an object can be shown on a graph with the x axis as the time and the y axis as the speed. Data points are plotted indicating the speed of the object at different times while it is traveling from one point to another. If the line is straight, then the acceleration was constant. The slope of the line represents the object’s acceleration. A steeper slope would indicate a faster acceleration. time in secondsdistance in meterstime in secondsdistance in meterstime in secondsdistance in meters10203040506070801001201 23 4 5 6789 10speed =20 m/sec10203040506070801001201 23 4 5 6789 1010203040506070801001201 23 4 5 6789 10no accelerationaccelerationdecelerationtime in secondsspeed m/sec10203040506070801001201 23 4 5 6789 10riserunfaster accelerationslope = rise/runacceleration = change of speed/timeAcceleration is the rate at which an object’s velocity changes. A change in velocity can bbbbbeeeeee annnnnnnnn iiiiiiiiiiiiiiinnnnnnnnnnnnnnnncccccccccreeeeeaaaaaaaaaaaassssssssssseeeeeeeeeeee or decreasssssssssseeeeeeeeeeeee iiiiiiiiiiiiiiiiinnnnnnnnnnnnnnnn speed, or a change in direction. A race car accelerates, gaining speed, when it starts a rrrrrrrrrrrraaaaaaaaaaaaaaacccccccccceeeeeeeeeeee. The cccaaaaaaaaaaaaarrrrrrrrrrrrrr ddddddddddddddeeeeeecccccccceeeeeeeeeeeeeellllllllleeeeeeeeeeeeratesss,,,,,,,, ooooooooooooooooooorrrrrrrr hhhhhhhhhhhhasssssssssssssssss negative acceleration, when it slows down and stops to re-fuel. A race car traveling aaaaaaaaaaaarrrrrrrrrrrrrrroooooooooouuuuuuuuuuuuuuunnnnnnnnnnnd the trackkkkkkk aaaaaaaaaaaaaattttttttttttt aaaaaaaaaaaaaa ccccconssssssssssstttttttttttaaaaaaaaaaaaaaaaannnnnnnnnnnnnt spppppppppppeeeeeeeeeeeeeeeeeeeeeeeeedddddddddddddalso has acceleration because it is changing direction.If an object is changing speed, but not changing direction, you can calculate acceleration. Basically, acceleration equals the change of speedof an object, . Imagine a roller coaster car at the peak of a steep drop. The initial speed of the car is 0 m/sec, and its speed at the bottom of the peak is 30 m/sec. It takes three seconds to travel from the top to the bottom. The roller coaster accelerated at 10 m/sec2.1020253035405055aaaaaaaaaaaaaacccccccccccccceeeeeeeeeeeeelllllleeeeeeeeeeeeeeeerrrrrrrrrraaaaaaaaaaaatttttttttiiiiiiooooooon ===== rrrcccccccccchhhhhhhhhhhhaaaaaaaaaaaaaaaaannnnnnnnnnnnnggggggggggggggggeeeeeeeeeeeeeee oooooooooooooofffffffffffff ssssssssssssssppppppppppppeedtimeinitial speed 0 m/sec333333333333333333300000000000000000 mmmmmmmmm/secaaaaaaaaaaaaaaacccccccccccccccccccccceeeeeeeeleratioooooooooooooonnnnnnnnnn = rr333300000000000000 mmmmmmmmmmmmmmmmmm/////////sss3 sec========= 110 m/sec2Accelerationdistance vs. timeeeeeeeeeeee ggggggggggrrrrrrrrrraaaaaaaaaaapppppppppppphhhhhhhhhhhhhhhh.. TTTTTTTTTTTTTThhhhhhhhhhhhhhhhhhhheeeeeeeeeeeeee ssssssssssllllllloooooooooooooopppppppppppppppppppe of the lllllllllllllllliiiiiiiiiiiiiinnnnnnnnnnnnnnnnnnnnneeeeeeeeeeee reeeeeeeeeeeeppppppppppppppppppppppprrrrrrrrrrrreeeeeeeeeeeeesssssssssseeeeeeeeeeeeennnnnnnnnnnnnnnttttttttttttttsssssssssss an object’s speed. A straight line indicates no change in speed, therefore the obbbjjjjjjjeecccccccttttttttt iiiiiiiiiiisssssssss nnnnnnnnnnnnnnoooooooooooootttttttttt aaaaaaaaaaacccccccccccccccccceeeeeeelllllllleratttttttttttttttiiiiiiiiinnnnnnnnnnng. AAAAAAAA indicates that the object’s speed is changing. A curve with a slope that’s getting steeeeeeeeeeeeeeeepppppppppppppppeeeeeeeeeeeeeerrrrrrr, tells us thhhhhhatttttt tttttttttttthhhhhhhhhhhhhheeeeeeeeeeee object iiiiiiiiisssssssssssss raaaaaaaaaaaaaaacccccccccccccccccccceeelllllllllllllleeeeeeeeeeeeeerrrrrrrrrrrrraaaaaaaaatttting. A line curved in the opposite direction indicates that the object is deceleratinnnnnnnnnnngggggggggggggggggg.Theeeeeeeeeeee aaaaaaaaaaaacccccceeeeeeeeeeellllllleeeeeeeeeeeerrrrrrrrrrrrrrraaaaaaaaaaaaaaaattttttttttttttttiiiiiiiiiiiioooooooonnnnnnnnnn oooooooooooooffffffff aaaaaaaaaaannnnnnnnnnn object cccccccaaaaaaaaaaannnnnnnnnnnnnnnn bbbbbbbbbbbe ssssssssssssshhhhhhhhhhhhhhhhhhhoooooooooooooooowwwwwwn on aaaaaaaaaaaaa ggggggggggggggggrrrrrrrrrrrrrraaaaph with the x axisasssssss ttttttttttttthhhhhhhhhee ttttttttiiiiiiiimmmmmmmmmmmmmmmmmmmmeeeeee aaaaaaaannnnnnnnnnnnndddddddddddddddd tttttttttthhhhhhhhhhhhhhhhheeeeeeeeeeeeee yyyyyyyyyyyyyyyy axxxxxxxxxxiiiiiiiiiiiiiiissssssssssss aaaaaaaaaaaaas the sppppppppeeeeeeeeeeeeeeeeeeeeeeeeeeedddddddddddd. DDDDDDDDDDDDDDDaaaaaaaaaaaaaaaattttttttttaaaaaaaaaaaa pppppoooooooooooiiiiiiiiiiiiiiinnnnnnnnnnnnnnnnnttts are plotted indicating tttttttttttthhhhhhhhhhhhhhhe ssssssssssspppppppppppppppppppppppppeeeeeeeeeeeeeeeeeeeeeeeedddddddddd oooooooooooooffffffffffffffff ttttttttttthhhhhhhhhhhhhhhhhhhheeeeeeee ooooooooooobbbbbbbbbbbbbbbbbbbjjjjjjjjjjeeeeeccttttttttttttt aaaaaaaaaaaaattttttttttt ddddddddiiiiiiffffffffffffffffffffffffffffeeeeeeeeeeeerrrrrrrrrrrrrrreeeeeeeeeeeeeennnnnt timeessssssssss wwwwwwwwwwwwwwwwwwwwhhhhhhhhhhhhiiiiilllllllllleeeeeeeeeeeeee iiiiiiiiiiiiittt is traveling from oooone ppppppppppppppooooooooooiiiiiiiiiiiiiinnnnnnnnnnttttt tttttttttttoooooooooo aaaaaaaaaaaaaannnnnnnnnnnnnnnnoooooooother. If thhhhheeeee lllllllllllliiiiiiiiiiiiiinnnnnnnnnnnneeeeeeeeeee iiiiiiisssssss ssssssssssssttttttttttrrrrrrrrraaaaaaaight, tttttttthhhhhhhhhhhhhhhhhhheeeeeeeeeeeeeeennnnnnnnnnnnnn the tacceleration was connsssssssssssttttttttttttaaaaaaaaaaaaaaaaannnnnnnnnnnntttttttttt... TTTTTTTTTTTTTTTTTTThhhhhhhhhhhe slope of the line rrrrrrrrreeeeeeeeeepppppppppppppppppprrrrrrrrrrrreeeeeeeesseeeeeeeeeennnnnnnnnnnnnnnnnttttttttttttsssssssssssss the ooooooobbbbbbbbbbbbbbbbbbbjjjjjjjjjjjeeeeeeeeeeecct’s acceleration. A steeeeeeeeeepppppppppppppppppeeeeeeeeeeeerrrrrrr slope would indicate a fastteeeerrrrrrrrrrr aaaaaaaaaaaaacccccccccccccccccccccceeeelllllllllllleeeeeeeeeeeeeeeerrrrrrrrraaaaaaaaaaaaaaaatttttttttttiiiiion. tttttttttttttttiiiime innnnn sssssssssssssseeeeeeeeeeeccccondsdistance in meterstime innnnnnnnnnnnnnn sssssssssecondsdddddddddddddddiiiiiiiiiissssstaaaaaaaaaaaannnnnnnnnnnnnccccccccceeeeeeeeee innnn mmmmmmmmmmmmmmeterrrrrrrrrrrrrsssssssssssstime in secondsdistance in meters10203040506070801001201 23 4544544454545455454455 6 7 89999989998 99810speed =200000000 mmmmmmmmmmmmm///////////ssssssssseeeeeeeeeeeeecccccccccspeed =20 mmmmmmmmm//sseeeeccdmmmmmmmpeed =2eee102030030300300333030303034040040404040404040440004506060606066060606006060607008088080880800800081010010001011000000000000000012222222221200000000001 23 45 67666689 1010203040506070801001201 23 45 6 7 89 10noo aaaaaaaaaaaaaaaaaccccccccccccccccccccccceeellllllllllleeeeeeeeeeeeeeerrrrrrrrrrrrrrraaaaaaaaattttttttttttttiiiiiiiiiiiiooooooooooooooooonnnnnnrrrrrrracceeeeeeeeeeeeeellllllllllllleeeeeeeeeeeeeeeeeeeeeerrrrrationdecelerationrriidspeed m/sec10203040506070801001201 23 45 6 7 89 10risesrunnfaster a e accelerc eationa o
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