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Kinematics Kinematics is the branch of mechanics that describes the motion of objects without necessarily discussing what causes the motion. We will learn to describe motion in three ways. – Using words – Using graphs – Using equations

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Particle A particle is an object that has mass but no volume and occupies a position described by one point in space. Physicists love to turn all objects into particles, because it makes the math a lot easier.

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Position How do we represent a point in space? a) One dimension b) Two dimensions c) Three dimensions

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objectposition change As an object moves, its position undergoes change Two quantities describe changing position Distance Displacement VS The length of the path traveled The length and direction of a straight line path from the beginning to the end position distance displacement Sometimes the path traveled is a straight line distance = displacement Displacement will never be greater than distance

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Distance (d) The total length of the path traveled by a particle is called distance. “How far have you walked?” is a typical distance question. The SI unit of distance is the meter.

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Displacement The change in the position of a particle in a certain direction Δ is a Greek letter used to represent “change in “. Δx therefore means “change in x”. It is always calculated by the final value minus the initial value “How far are you from home” is a typical displacement question The SI unit for displacement is the meter Calculation of displacement

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A B 50 m displacement 100 m distance Distance vs Displacement A picture can help you distinguish between distance and displacement.

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STOP Vectors and scalars Quantities that have both size, also called magnitude, and direction, are called vectors. Displacement is a change in position in a certain direction. It is a vector quantity. Quantities that are just magnitude, numbers without any direction, such as distance, time, or temperature, are called scalars.

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In one dimensional motion, displacement direction the displacement direction is often given positivenegative as positive (+) or negative ( displacement + A displacement of +3.5 m implies movement of positive 3.5 m in the positive direction. displacement A displacement of 3.5 m implies movement of negative 3.5 m in the negative direction. Positivenegative Positive and negative directions are arbitrarily chosen arbitrarily, but usually agree with standard mathematical conventions.

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Question True or False: An object can be moving for 10 seconds and still have zero displacement. a. Trueb. false If the above statement is true, then describe an example of such a motion. If the above statement is false, then explain why it is false.

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Question A cross-country skier moves from location A to location B to location C to location D. Each leg of the back-and-forth motion takes 1 minute to complete; the total time is 3 minutes. a. What is the distance traveled by the skier during the three minutes of recreation? b. What is the net displacement of the skier during the three minutes of recreation?

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Example You are driving a car on a circular track of diameter 40 meters. After you have driven around 2 ½ times, how far have you driven, and what is your displacement?

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average velocity The average velocity of an object is defined as ratiochange in position the ratio of its change in position to the time taken to change the position time taken to change the position. v v m/s v = average velocity; in units of m/s = x x x = change in position, or displacement; m in units of m t t s t = change in time; in units of s It is the rate at which displacement occurs Velocity is a vector quantity

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positive sign A positive sign indicates movement positive direction in the positive direction. negative sign A negative sign indicates movement negative direction in the negative direction. The “sign” of the velocity indicates the direction of movement.

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Speed Speed is the magnitude of velocity. scalar It is a scalar and has no direction given with it. Average speedtotal distance Average speed is the total distance traveled divided by total time divided by the total time taken. Average velocitytotal displacement Average velocity is the total displacement divided by total time divided by the total time taken. Average speed and average velocity are not always equivalent because total distance and total displacement are not always the same. absolute value Speed is the absolute value of velocity. positive It is always a positive value.

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Example How long will it take the sound of the starting gun to reach the ears of the sprinters if the starter is stationed at the finish line for a 100 m race? Assume that sound has a speed of about 340 m/s.

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Example You drive in a straight line at 10 m/s for 1.0 km, and then you drive in a straight line at 20 m/s for another 1.0 km. What is your average velocity?

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Acceleration (a) Any change in velocity over a period of time is called acceleration. The sign (+ or -) of acceleration indicates its direction. Acceleration is occurring when an object… – speeds up – slows down – Turns (changes direction)

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Questions If acceleration is zero, what does this mean about the motion of an object? Is it possible for a racecar circling a track to have zero acceleration?

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Average Acceleration Average Acceleration. In AP Physics B we only consider situations where acceleration is constant. This allows us to use the following formula a a a = average acceleration; in units of m/s 2 = vfvfvfvf v f m/s v f = final velocity; in units of m/s v i m/s v i = initial velocity; in units of m/s t t s t = time for the change to occur; in units of s - vivivivi v f – v i = change in velocity

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Acceleration in 1-D Motion has a sign! If the sign of the velocity and the sign of the acceleration is the same, the object speeds up. If the sign of the velocity and the sign of the acceleration are different, the object slows down.

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Kinetics Equations

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Example You are designing an airport for small planes. One kind of airplane that might use this airfield must reach a speed before takeoff of at least 28 m/s, and can accelerate at 2.00 m/s 2. What must the minimum length of the runway be?

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Example A car traveling at 90 km/h strikes a tree. The front end of the car compresses and the driver comes to a rest after traveling 0.80 m. How long did it take the car to come to a stop?

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