P2Week7 - Week 7 Motion in Two Dimensions Sections 3.1 3.3...

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1 Week 7 Motion in Two Dimensions Sections 3.1 – 3.3 Motion in Two Dimensions Using + or – signs is not always sufficient to fully describe motion in more than one dimension Vectors can be used to more fully describe motion Will look at vector nature of quantities in more detail Still interested in displacement, velocity, and acceleration Will serve as the basis of multiple types of motion in future chapters
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2 Position and Displacement The position of an object is described by its position vector, The displacement of the object is defined as the change in its position r Δ f i r r r General Motion Ideas In two- or three-dimensional kinematics, everything is the same as as in one- dimensional motion except that we must now use full vector notation Positive and negative signs are no longer sufficient to determine the direction
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3 Average Velocity The average velocity is the ratio of the displacement to the time interval for the displacement The direction of the average velocity is the direction of the displacement vector The magnitude of the instantaneous velocity vector is the speed The speed is a scalar quantity v ave = r f r i t f t i = Δ r Δ t Average Acceleration The average acceleration of a particle as it moves is defined as the change in the instantaneous velocity vector divided by the time interval during which that change occurs. As a particle moves, the direction of the change in velocity is found by vector subtraction The average acceleration is a vector quantity directed along Δ = Δ f i avg f i t t t v v v a Δ = f i v v v Δ v
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4 Instantaneous Velocity The instantaneous velocity is the limit of the average velocity as Δ t approaches zero Equals the derivative of the position vector with respect to time Δ → Δ = Δ 0 lim t d t dt r r v The instantaneous acceleration is the limiting value of average acceleration as Δ t approaches zero Equals the derivative of the velocity vector with respect to time Δ → Δ = Δ 0 lim t d t dt v v a Producing An Acceleration Various changes in a particle’s motion may produce an acceleration The magnitude of the velocity vector may change The direction of the velocity vector may change Even if the magnitude remains constant Both may change simultaneously
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5 Clicker quick question 1 Which of the following cannot possibly be accelerating? (A) An object moving with a constant speed (B) An object moving with a constant velocity (C) An object moving along a curve (D) An object moving along a straight line (E) Both B and D Clicker quick question 2 You tie a stone with a string and whirl it around in a circle. The acceleration of this stone is:
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P2Week7 - Week 7 Motion in Two Dimensions Sections 3.1 3.3...

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