Mechanics Motion How do we describe the motion of an object Where is it located at a given time Position How far does an object move Distance or displacement How fast does it move from one place to another Speed or velocity Does how fast it move change over time Acceleration Position and Distance Need a coordinate system 1 D What can we say about this motion What is the object s position at t 2s t 5s x 1m x 2 5m What distance does the objet travel between these two times distance 1 5m Average Speed A measure of the distance covered to the time it takes to cover that distance Average Speed Distance Covered Time Units m s km h ft s cm s mi h Direction doesn t matter Always a positive number Example What is the average speed of the object for the time interval between t 2s and t 5s Same graph as previously Distance covered 1 5m Time interval 3 s Average speed 1 5m 3s 0 5m s What is the average speed of the object below for the time interval shown Distance 4m Time 8s Average speed 4m 8s 0 5m s When the object s motion is uniform the object covers the same distance each second Can you predict the distance the object will have traveled at a time t 20s Average speed distance time 0 5m s distance 20s Distance 10m Graphical Representation Constant speed covers the same distance each second 0 5m s What would the graph look like if the object were traveling faster Steeper slope Slower Less steep What would the graph look like if the object was traveling in the negative direction Negative slope Distance vs Displacement Distance how far scaler quantity how much Displacement how far from start to finish and directed along the line connecting start to finish vector quantity how much and what direction Displacement Direction in 1 D positive or negative Displacement x x f x i 12m 4m 8m vector points in positive direction or 4m 12m 8m vector points in negative direction Distance vs Displacement Is it possible for the amount of displacement to be different than the distance covered Yes but displacement can never be bigger than distance traveled Is it possible for the object to cover some distance and have zero displacement Yes by ending where you started Average Velocity A measure of the displacement covered in a certain amount of time Vector quantity how fast and what direction Average Velocity Displacement Time V x or v x f x i t t f t i Positive Velocity or Negative Velocity or down Example In the figure below an object s position is given every second Determine the average velocity in the time interval between t 1s and t 2s V x f x i t 4m 1m 1s 3m 1s 3m s Determine the average velocity in the time interval between t 2s and t 3s V x f x i t 9m 4m 1s 5m 1s 5m s Is the velocity constant No it s increasing What would the graphical representation look like Relationship between Graphs Slope of position verse time graph is equal to the velocity at that particular position By examining the slope of the position of the position verse time graph one can determine the velocity is Positive or negative Increasing decreasing or constant Instantaneous Speed and Velocity Instantaneous Speed The same as the average speed except for a very very short time interval The speed of an object at a particular instant in time You do not need to use a formula The speed that you read on your speedometer Instantaneous Velocity Instantaneous speed with direction Varying Speeds In the figure below what can we say about the speed of the object at the various positions indicated A B slope decreasing speed is decreasing slope positive moving in positive direction B C same as A B at C slope is 0 speed is 0m s C D slope becomes steeper but negative speed is increa sing but movin g in negati ve directi on Accele ration Measures how the motion of an object changes Change in the speed Change in the direction In particular measures how quickly slowly the velocity changes Large acceleration velocity changes quickly Small acceleration velocity changes slowly Acceleration is a vector quantity 1 D Same sign as velocity speeding up Opposite sign as velocity slowing down decelerating A measure of the rate at which the velocity changes in a given time interval acceleration change in velocity time interval Formula a v or a v f v i t t Units m s 2 When an object accelerates does it cover the same distance each second No Does it cover more distance If it s speeding up Less distance If it s slowing down When an object is accelerating the position verse time graph will have some curve to it it will not be a straight line from what we learned in the pervious slides A cart on a track is traveling at a speed of 5 m s in the positive x direction After a time of 4 seconds the speed has decreased to 3 m s What is the acceleration of the cart Does the sign positive negative make sense according to the motion a v f v i t t 4 seconds v i 5 m s v f 3 m s a 3 5 4 Example a 2 4 a 0 5 m s 2 slowing down Constant Acceleration Velocity increases decreases at a constant rate Gravitational Acceleration Constant acceleration as an object is released on Earth Assumes no air resistance or friction Acceleration is constant in the vertical direction Speed increases decreases at a constant rate Acceleration due to gravity 9 8 m s 2 g decreases with increasing altitude g varies with latitude 9 80 m s 2 is the average at the Earth s surface use 10 m s 2 for homework use 9 8 m s 2 in lab Freely Falling Objects A freely falling object is any object moving freely under the influence of gravity alone no outside push or pull The acceleration of an object in free fall is directed downward regardless of initial motion We will use a g 10 m s 2 for purposes of visualization The negative sign implies a downward direction Example Two balls are dropped from the same height The second ball is twice as heavy as the first ball Which of the statements is true The balls will hit the ground at the same time If you drop an object in the absence of air resistance it accelerates downward If you throw it downward its downward acceleration after release is still 9 8 m s 2 A ball is throw straight upward with a speed of 5 m s after being released its acceleration will be 9 8 m s 2 Dropping an Object The acceleration is in the same direction as the motion and therefore the velocity continually increases at a constant rate At the top of the motion the velocity …