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## One Dimensional Motion

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**One Dimensional Motion**Frames of Reference Distance and Displacement Speed and Velocity Graphical Relations**Motion may seem simple enough, but physics is able to make**it more complicated then you could imagine • Our first topic will be motion in one dimension • That includes motion along a straight line either going left and right or up and down Kinematics: Motion in Physics**Watch my movements carefully …**A lesson in observation…**Watch my movements carefully …**• Keep watching … A lesson in observation…**Watch my movements carefully …**• Keep watching … • Keep watching … A lesson in observation…**Watch my movements carefully …**• Keep watching … • Keep watching … • How much did I move? • ~1 cm? • ~1 m? • ~1 km? A lesson in observation…**If I had to estimate I would say in the past 8 seconds I**moved approximately 10,000 km • If you missed it you must not be paying close enough attention or maybe you blink too long A lesson in observation…**It would be much too complicated and tedious to consider all**these other motions so we choose a frame of reference for motion that ignores those • You can usually choose your frame of reference so that the starting point is the origin and it makes problems slightly easier Frames of Reference**I want the right half of the room to close your eyes until I**tell you to open them • I want the left half of the room to keep your eyes open and pay attention to my motion • Ready … More strange observations…**Right half of the room, how much did I move?**• Left half of the room, how much did I move? • In Physics we need a way to differentiate between what the right side of the room saw and the left side of the room Motion**We have two terms to describe an object’s movement**• Distance: the actual length traveled by an object regardless of direction • Displacement: the difference between an objects final position and initial position • Δx = xf - xi • Notice that displacement can be negative or positive Distance versus Displacement**Coach Seabolt makes the soccer players run the field (~100**meters long) 7 times. • What is the distance traveled by a player? • What is the displacement of a player? Simple Example**The ground moves 8 cm in a certain region. What happened?**Is displacement all we need to know?**The time it takes for the displacement to happen is just as**important as the change in position Something else is important in motion**Velocity: the displacement of an object divided by the time**in which the displacement occurs • Velocity = Δx/Δt (CAN ONLY BE USED WHEN VELOCITY IS CONSTANT!) • Just like displacement can be negative, velocity can also be negative • How do we decide if velocity is negative or positive? Calculating Velocity**Speed**• Have you ever seen a car that has negative numbers on the speedometer? • That’s because a car doesn’t care about the direction only how fast • Speed: the distance traveled divided by the time • Speed = distance/time**Instantaneous**• The value of a physical variable at a particular moment or instant • Average • The value of a physical variable over a given period of time Instantaneous versus Average**How are displacement and velocity related graphically?**• Given a graph of position versus time, how can you determine the velocity and vice versa? • Let’s look at a simple example …**Displacement -> Velocity**• The motion of a car is represented in the graph to the right. • Rank the velocity of the car at the four points given. • How did you know this?**The velocity of an object is equal to the slope of the**displacement versus time graph! • Average Velocity – Slope between two points • Instantaneous Velocity – Slope along a line containing the point • In fact, anytime you want to divide two variables on a graph, take the slope! Displacement -> Velocity**The two graphs to the right represent the velocity of two**cars. • Which car traveled further, car A or Car B? Velocity -> Displacement**The displacement of an object is equal to the area of the**velocity versus time graph between the graph and the x-axis! • In fact, anytime you want to multiply two variables on a graph, find the area between the curve and the x-axis! Velocity -> Displacement**Consider the following:**• I slow down from 20 m/s to 0 m/s • What just happened? So is displacement and velocity all we need to know?**The time it takes to change from your initial velocity to**your final velocity is also important Something else is important other than change in velocity**As always it is important to understand what the units are**using dimensional analysis: • Try to determine the units of acceleration given the following formula: • Acceleration = Δvelocity Δtime Acceleration = meters/second second Acceleration = meters = m second2 s2 What are the units of acceleration?**A car traveling at 7 m/s accelerates at 2.5 m/s2 to reach a**speed 17 m/s. How long does the acceleration take? • With an acceleration of -1.2 m/s2 how long will it take a bike to stop if it is initially moving at 6.5 m/s? • Problem 1: 4 seconds • Problem 2: ~5.4 seconds Try these simple examples…**Remember, positive and negative signs ONLY indicate**DIRECTION! • With this in mind, determine what happens given the following: Positive and Negative Acceleration**What does negative or positive acceleration mean?**• Imagine two cars traveling down a highway in opposite directions. What is the sign of the velocity of each of the cars?**Assume that we are going to give each car a positive**acceleration. • The question of the day is what direction would a positive acceleration be pointing? Lets accelerate the cars…**Positive acceleration is to the north!**• Notice the direction of the velocity compared to the direction of the acceleration. Acceleration does not mean speeding up!!! It just means a change in velocity!!! Which car has a decreasing velocity?**Positive acceleration is to the north!**• Car 1 is increasing its velocity and Car 2 is decreasing its velocity. Sound confusing? It shouldn’t be, at least if you pay attention to the direction of the arrows!**Instead of giving it a positive acceleration, let’s give**the cars a negative acceleration • Remember that a negative acceleration does not mean you are slowing down, the negative is only telling you the direction! Let’s look at the other direction…**Negative acceleration is south!**• This time Car 2 has an increasing velocity while Car 1 has a decreasing velocity. Don’t forget the negative sign just tells you direction, it doesn’t mean slowing down!!!