lecturenotes-Jan20

lecturenotes-Jan20 - Motion with Constant Acceleration The...

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Unformatted text preview: Motion with Constant Acceleration The acceleration a is a constant. The v ( t ) versus t plot is a straight line with slope = a and intercept = v . The x ( t ) versus t plot is a parabola that intercepts the vertical axis at x = x . v avg = v + v 2 x − x = v + v 2 t Consider the graph the position versus time graph shown. Which curve on the graph best represents a constantly accelerating car? a) A b) B c) C d) D e) None of the curves represent a constantly accelerating car. Example Consider the graph the position versus time graph shown. Which curve on the graph best represents a car that is initially moving in one direction and then reverses directions? a) A b) B c) C d) D e) None of the curves represent a car moving in one direction then reversing its direction. Example In physics we have parameters that can be completely described by a number and are known as scalars . Temperature and mass are such parameters. Other physical parameters require additional information about direction and are known as vectors . Examples of vectors are displacement, velocity, and acceleration. In this chapter we learn the basic mathematical language to describe vectors. In particular we will learn the following: Geometric vector addition and subtraction Resolving a vector into its components The notion of a unit vector Addition and subtraction vectors by components Multiplication of a vector by a scalar The scalar (dot) product of two vectors The vector (cross) product of two vectors An example of a vector is the displacement vector, which describes the change in position of an object as it moves from point A to point B . This is represented by an arrow that points from point A to point B . The length of the arrow is proportional to the displacement magnitude. The direction of the arrow indicated the displacement direction. The three arrows from A to B , from A' to B' , and from A'' to B'' , have the same magnitude and direction. A vector can be shifted without changing its value if its length and direction are not changed. In books vectors are written in two ways: Method 1: (using an arrow above) Method 2: a (using boldface print) The magnitude of the vector is indicated by italic print: a . Geometric Vector Addition (3-3) Geometric Vector Addition (3-3) Geometric Vector Subtraction Note: We can add and subtract vectors using the method of components. For many applications this is a more convenient method. A B C Unit Vectors A unit vector is defined as a vector that has magnitude equal to 1 and points in a particular direction. A unit vector is defined as a vector that has magnitude equal to 1 and points in a particular direction. Unit vectors lack units and their sole purpose is to point in a particular direction. The unit vectors along the , , and axes are labeled , , and , resp ˆ e ˆ ˆ i j ctiv ly. k e x y z Unit vectors are used to express other vectors For example vector can be written as ....
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lecturenotes-Jan20 - Motion with Constant Acceleration The...

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