Topic 1 1D Motion PHYSICS 231 Key Concepts 1D motion Particle model Position Coordinate system 1 axis with positive and negative direction Displacement Velocity rate of change of position can have positive or negative direction Acceleration rate of change of velocity can have positive or negative direction Average velocity acceleration vs instantaneous Equations for X t and v t for constant acceleration Gravity on the surface of the earth provides an acceleration of g 9 81 m s2 if no other forces are acting free fall towards the center of the earth Concept of free fall 01 14 2019 Physics 231 Spring 2011 2 Key concepts ctd Displacement vs time x t Graph Slope is velocity sign Velocity vs time v t Graph Area under curve is displacement x sign change in position Slope is acceleration sign Acceleration vs time a t Graph Area under the curve is change of velocity v sign Understand how to derive one graph from another 01 14 2019 Physics 231 Spring 2011 3 Clicker question Distance between snapshots in motion diagram A increases B stays the same C decreases 01 14 2019 Physics 231 Spring 2011 4 Position For 1D motion we need to define a one axis coordinate system an x axis along the path of motion particle model The axis features Labeled using units of length for example meters Zero is chosen at your convenience Positive direction we agree in this class that positive direction will always be to the right or up Position of an object is the value of the axis label at its location We use here the symbol x Position may change with time It is a function of time x t 01 14 2019 Physics 231 Spring 2011 5 Position vs time diagram A moving object has a position at each point in time Graph position as a function of time function x t x 4m 3m 2m 1m t 1 m 01 14 2019 0s 1s 2s Physics 231 Spring 2011 6 Displacement Displacement is a change in position Suppose there is an initial position at an earlier time x i and a final position at a later time xf The displacement Dx for this particular part of the motion is Dx xf xi Note this can be positive or negative it has a direction If the change is towards a larger number positive direction of the axis x f is larger than xi and Dx will be positive If the change is towards a smaller number negative direction of the axis xf is smaller than xi and Dx will be negative Dx is ONE symbol just like x or y 01 14 2019 Physics 231 Spring 2011 7 Quiz Maria stands at position x 30 m 10 s later she is located at position x 20 m What was her displacement A 50 m B 20 m C 0 m D 20 m E 50 m 01 14 2019 Physics 231 Spring 2011 8 Velocity Velocity is rate of change of position The average velocity for a specific part of an object s motion beginning at time ti initial time ending at a later time tf final time is Average Velocity Displacement Time interval with symbols x v t With Dt tf ti Unit m s others km h miles h Velocity has a sign and therefore a direction its the sign of Dx because Dt is always positive Motion towards positive x axis positive velocity Motion towards negative x axis negative velocity Magnitude of velocity v is also called speed Distance travelled Average Speed Time interval 01 14 2019 Physics 231 Spring 2011 9 Quiz Maria stands at position x 30 m 10 s later she is located at position x 10 m What was her average velocity A 2 m s B 3 m s C 0 m s D 3 m s E 2 m s 01 14 2019 Physics 231 Spring 2011 10 Quiz Maria stands at position x 30 m In 10s she walks to x 50 m In 20 s she then walks back to x 30 m What was her average velocity A 1 5 m s B 1 33 m s C 0 m s D 1 33 m s E 1 5 m s 01 14 2019 Physics 231 Spring 2011 11 Clicker question Maria stands at position x 30 m In 10s she walks to x 50 m In 20 s she then walks back to x 30 m What was her average speed A 1 5 m s B 1 3 m s C 0 m s D 1 3 m s E 1 5 m s 01 14 2019 Physics 231 Spring 2011 12 Instantaneous velocity Officer it took me 1 h to go 25 miles so my average speed was only 25 mph Instantaneous speed speed at one point in time averaged over very small time interval 01 14 2019 Physics 231 Spring 2011 13 Velocity in position vs time graph What is the instantaneous velocity at t 2 0 s D x t The velocity at one point in time is the slope of the tangent to the x t curve at that time Calculate slope of green curve x v t x t What is the average velocity for motion from t 0s to t 5 0s Calculate slope of red curve http www math umn edu garrett qy TraceTangent html 01 14 2019 Physics 231 Spring 2011 14 v m s v m s t 1 v 2 t 1 v 2 2 0 2 0 0 T s 0 1 What is the distance covered in 1 second 2 What is the area indicated by The area under the v t curve is equal to the displacement of the object Note unit of area area 2m s 1s 2m PHY 231 T s Q 1 2 a b c d 1 2 1 2 1 1 2 2 15 Acceleration Acceleration is the rate of change of velocity NOTE This word is used differently from everyday use Acceleration can mean increase decrease or change of direction of velocity When the velocity does not change the acceleration is zero If velocity changes from vi at time ti to vf at time tf then the average acceleration a is v f v i v a t f ti t Unit m s2 01 14 2019 Physics 231 Spring 2011 16 Sign of acceleration As vi and vf can each be positive or negative acceleration can also be positive or negative The sign indicates the direction of the change of velocity If velocity becomes smaller more negative then the acceleration is negative vf vi If velocity becomes larger more positive then the acceleration is positive vf vi Note that negative acceleration DOES NOT mean the object gets slower Example if a car s velocity changes from 10 m s to 30 m s the car is getting faster moving in negative x direction and the acceleration is negative as the velocity becomes smaller 01 14 2019 Physics 231 Spring 2011 17 Clicker question A car is moving to the right and …
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