{"id":1400,"date":"2018-02-06T15:40:28","date_gmt":"2018-02-06T15:40:28","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-osuniversityphysics\/?post_type=chapter&p=1400"},"modified":"2018-02-06T15:40:28","modified_gmt":"2018-02-06T15:40:28","slug":"3-chapter-review","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-osuniversityphysics\/chapter\/3-chapter-review\/","title":{"raw":"3 Chapter Review","rendered":"3 Chapter Review"},"content":{"raw":"
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Key Terms<\/h3>\r\n
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acceleration due to gravity<\/strong><\/dt>\r\n \t
acceleration of an object as a result of gravity<\/dd>\r\n<\/dl>\r\n
\r\n \t
average acceleration<\/strong><\/dt>\r\n \t
the rate of change in velocity; the change in velocity over time<\/dd>\r\n<\/dl>\r\n
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average speed<\/strong><\/dt>\r\n \t
the total distance traveled divided by elapsed time<\/dd>\r\n<\/dl>\r\n
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average velocity<\/strong><\/dt>\r\n \t
the displacement divided by the time over which displacement occurs<\/dd>\r\n<\/dl>\r\n
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displacement<\/strong><\/dt>\r\n \t
the change in position of an object<\/dd>\r\n<\/dl>\r\n
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distance traveled<\/strong><\/dt>\r\n \t
the total length of the path traveled between two positions<\/dd>\r\n<\/dl>\r\n
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elapsed time<\/strong><\/dt>\r\n \t
the difference between the ending time and the beginning time<\/dd>\r\n<\/dl>\r\n
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free fall<\/strong><\/dt>\r\n \t
the state of movement that results from gravitational force only<\/dd>\r\n<\/dl>\r\n
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instantaneous acceleration<\/strong><\/dt>\r\n \t
acceleration at a specific point in time<\/dd>\r\n<\/dl>\r\n
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instantaneous speed<\/strong><\/dt>\r\n \t
the absolute value of the instantaneous velocity<\/dd>\r\n<\/dl>\r\n
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instantaneous velocity<\/strong><\/dt>\r\n \t
the velocity at a specific instant or time point<\/dd>\r\n<\/dl>\r\n
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kinematics<\/strong><\/dt>\r\n \t
the description of motion through properties such as position, time, velocity, and acceleration<\/dd>\r\n<\/dl>\r\n
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position<\/strong><\/dt>\r\n \t
the location of an object at a particular time<\/dd>\r\n<\/dl>\r\n
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total displacement<\/strong><\/dt>\r\n \t
the sum of individual displacements over a given time period<\/dd>\r\n<\/dl>\r\n
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two-body pursuit problem<\/strong><\/dt>\r\n \t
a kinematics problem in which the unknowns are calculated by solving the kinematic equations simultaneously for two moving objects\u00a0<\/span><\/dd>\r\n<\/dl>\r\n<\/div>\r\n<\/div>\r\n
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Key Equations<\/h3>\r\n<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Displacement<\/td>\r\n\u0394<\/span>x<\/span>=<\/span>x<\/span>f<\/span><\/span>\u2212<\/span>x<\/span>i<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u0394x=xf\u2212xi<\/span><\/span><\/td>\r\n<\/tr>\r\n
Total displacement<\/td>\r\n\u0394<\/span>x<\/span>Total<\/span><\/span><\/span>=<\/span>\u2211<\/span>\u0394<\/span>x<\/span>i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u0394xTotal=\u2211\u00a0\u0394xi<\/span><\/span><\/td>\r\n<\/tr>\r\n
Average velocity<\/td>\r\nv<\/span>\u2013<\/span><\/span>=<\/span>\u0394<\/span>x<\/span><\/span>\u0394<\/span>t<\/span><\/span><\/span>=<\/span>x<\/span>2<\/span><\/span>\u2212<\/span>x<\/span>1<\/span><\/span><\/span>t<\/span>2<\/span><\/span>\u2212<\/span>t<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v\u2013=\u0394x\u0394t=x2\u2212x1t2\u2212t1<\/span><\/span><\/td>\r\n<\/tr>\r\n
Instantaneous velocity<\/td>\r\nv<\/span>(<\/span>t<\/span>)<\/span>=<\/span>d<\/span>x<\/span>(<\/span>t<\/span>)<\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v(t)=dx(t)dt<\/span><\/span><\/td>\r\n<\/tr>\r\n
Average speed<\/td>\r\nAverage speed<\/span>=<\/span>s<\/span>\u2013<\/span><\/span>=<\/span>Total distance<\/span><\/span>Elapsed time<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>Average speed=s\u2013=Total distanceElapsed time<\/span><\/span><\/td>\r\n<\/tr>\r\n
Instantaneous speed<\/td>\r\nInstantaneous speed<\/span>=<\/span>\u2223\u2223<\/span>v<\/span>(<\/span>t<\/span>)<\/span><\/span>\u2223\u2223<\/span><\/span><\/span><\/span><\/span><\/span><\/span>Instantaneous speed=|v(t)|<\/span><\/span><\/td>\r\n<\/tr>\r\n
Average acceleration<\/td>\r\na<\/span>\u2013<\/span><\/span>=<\/span>\u0394<\/span>v<\/span><\/span>\u0394<\/span>t<\/span><\/span><\/span>=<\/span>v<\/span>f<\/span><\/span>\u2212<\/span>v<\/span>0<\/span><\/span><\/span>t<\/span>f<\/span><\/span>\u2212<\/span>t<\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a\u2013=\u0394v\u0394t=vf\u2212v0tf\u2212t0<\/span><\/span><\/td>\r\n<\/tr>\r\n
Instantaneous acceleration<\/td>\r\na<\/span>(<\/span>t<\/span>)<\/span>=<\/span>d<\/span>v<\/span>(<\/span>t<\/span>)<\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a(t)=dv(t)dt<\/span><\/span><\/td>\r\n<\/tr>\r\n
Position from average velocity<\/td>\r\nx<\/span>=<\/span>x<\/span>0<\/span><\/span>+<\/span>v<\/span>\u2013<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span><\/span>x=x0+v\u2013t<\/span><\/span><\/td>\r\n<\/tr>\r\n
Average velocity<\/td>\r\nv<\/span>\u2013<\/span><\/span>=<\/span>v<\/span>0<\/span><\/span>+<\/span>v<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>v\u2013=v0+v2<\/span><\/span><\/td>\r\n<\/tr>\r\n
Velocity from acceleration<\/td>\r\nv<\/span>=<\/span>v<\/span>0<\/span><\/span>+<\/span>a<\/span>t<\/span><\/span>(<\/span>constant<\/span><\/span>a<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>v=v0+at(constanta)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Position from velocity and acceleration<\/td>\r\nx<\/span>=<\/span>x<\/span>0<\/span><\/span>+<\/span>v<\/span>0<\/span><\/span>t<\/span>+<\/span>1<\/span>2<\/span><\/span>a<\/span>t<\/span>2<\/span><\/span><\/span>(<\/span>constant<\/span><\/span>a<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>x=x0+v0t+12at2(constanta)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Velocity from distance<\/td>\r\nv<\/span>2<\/span><\/span>=<\/span>v<\/span>2<\/span>0<\/span><\/span>+<\/span>2<\/span>a<\/span>(<\/span>x<\/span>\u2212<\/span>x<\/span>0<\/span><\/span><\/span>)<\/span><\/span><\/span>(<\/span>constant<\/span><\/span>a<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>v2=v02+2a(x\u2212x0)(constanta)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Velocity of free fall<\/td>\r\nv<\/span>=<\/span>v<\/span>0<\/span><\/span>\u2212<\/span>g<\/span>t<\/span><\/span>(positive upward)<\/span><\/span><\/span><\/span><\/span><\/span>v=v0\u2212gt(positive upward)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Height of free fall<\/td>\r\ny<\/span>=<\/span>y<\/span>0<\/span><\/span>+<\/span>v<\/span>0<\/span><\/span>t<\/span>\u2212<\/span>1<\/span>2<\/span><\/span>g<\/span>t<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>y=y0+v0t\u221212gt2<\/span><\/span><\/td>\r\n<\/tr>\r\n
Velocity of free fall from height<\/td>\r\nv<\/span>2<\/span><\/span>=<\/span>v<\/span>2<\/span>0<\/span><\/span>\u2212<\/span>2<\/span>g<\/span>(<\/span>y<\/span>\u2212<\/span>y<\/span>0<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>v2=v02\u22122g(y\u2212y0)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Velocity from acceleration<\/td>\r\nv<\/span>(<\/span>t<\/span>)<\/span>=<\/span>\u222b<\/span>a<\/span>(<\/span>t<\/span>)<\/span>d<\/span>t<\/span>+<\/span>C<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v(t)=\u222ba(t)dt+C1<\/span><\/span><\/td>\r\n<\/tr>\r\n
Position from velocity<\/td>\r\nx<\/span>(<\/span>t<\/span>)<\/span>=<\/span>\u222b<\/span>v<\/span>(<\/span>t<\/span>)<\/span>d<\/span>t<\/span>+<\/span>C<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x(t)=\u222bv(t)dt+C2<\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/section><\/div>\r\n<\/div>\r\n<\/div>\r\n
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Summary<\/span><\/h3>\r\n
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3.1<\/span>\u00a0<\/span>Position, Displacement, and Average Velocity<\/span><\/h4>\r\n