PHYSICS 1408 LAMP CHAPTER 2 NOTES ONE DIMENSIONAL MOTION Kinematics Equation Symbols Acceleration Velocity Position Time a v x t Initial and Final values are represented with subscripts such as VI and Vf Xi and Xf Kinematics Equations to Memorize Vf Vi at Vavg Vi Vf 2 Does not need X Xf Xi Vit 1 2 at2 Does not need Vf Vf 2 Vi 2 2a Xf Xi Does not need t Examples 1 A car with initial velocity of 10 m s accelerates Its velocity after 5 seconds is 20 m s What was the car s acceleration Given Vi 10 m s Solving for a Vf 20 m s T 5 s The kinematics equation with the variables given and needed is Vf Vi at Now plug in givens and solve 20 m s 10 m s a 5s 10 m s 5s a 2 m s2 a The car is accelerating at a rate of 2 m s2 2 A car going 20 m s comes to a stop in 30 m What is the acceleration Given Vi 20 m s Solving for a X 30 m Vf 0 m s Xf Xi Car came to a stop The kinematics equation we need is Vf 2 Vi 2 2a X Plug and Chug 0 m s 2 20 m s 2 2a 30 m 0 400 m s 60 s a 400 m s 60 s a 6 66 m s2 a The value is negative because the car is slowing down The car is accelerating at a rate of 6 66 m s2 3 A car is initially moving with a velocity of 10 m s It accelerates for 5 seconds at a rate of 2 m s2 If its final velocity is 20 m s over what distance was the car accelerating Given Vi 10 m s Solving For X Vf 20 m s A 2 m s2 T 5 s The kinematics equation we need is Xf Xi Vit 1 2 at2 Plug and Chug Xf Xi 10 m s 5 s 1 2 2 m s2 5 s 2 Xf Xi becomes X X 50 m 25 m X 75 m The car is accelerating over 75 meters Position Velocity Acceleration Charts Position velocity and acceleration can be compared as graphs over time The three graphs represent the linear relationships of x v and a Mathematically a d dx v d2 dx x Acceleration is the derivative of velocity which is the derivative of position One graph can help determine the other two graphs and show what is happening to each variable over the course of the problem These graphs represent a situation in which an object is moving at a positive velocity with a constant positive acceleration As you can imagine the graphs can vary quite a bit depending on the situation they re depicting
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