The polar coordinates of a certain point are (r = 3.15 cm, 0 = %3D 262°). (a) Find its Cartesian coordinates x and y. x = |-0.438 ст %3D -0.312 Your response is off by a multiple of ten. cm (b) Find the polar coordinates of the points with Cartesian coordinates (-x, y). = 1.41 Your response differs from the correct answer by more than 10%. Double check your calculations. cm = |-45 Your response differs from the correct answer by more than 10%. Double check your calculations. (c) Find the polar coordinates of the points with Cartesian coordinates (-2x, –2y). = 2.83 Your response differs from the correct answer by more than 10%. Double check your calculations. cm = 225 The response you submitted has the wrong sign. (d) Find the polar coordinates of the points with Cartesian coordinates (3x, -3y).
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
![**Polar and Cartesian Coordinates Exercise**
The polar coordinates of a certain point are given as \( r = 3.15 \, \text{cm}, \theta = 262^\circ \).
**(a) Find its Cartesian coordinates \( x \) and \( y \).**
- \( x = -0.438 \, \text{cm} \) ✔️
- \( y = -0.312 \, \text{cm} \) ✖️
- *Your response is off by a multiple of ten.*
**(b) Find the polar coordinates of the points with Cartesian coordinates \((-x, y)\).**
- \( r = 1.41 \, \text{cm} \) ✖️
- *Your response differs from the correct answer by more than 10%. Double check your calculations.*
- \( \theta = -45^\circ \) ✖️
- *Your response differs from the correct answer by more than 10%. Double check your calculations.*
**(c) Find the polar coordinates of the points with Cartesian coordinates \((-2x, -2y)\).**
- \( r = 2.83 \, \text{cm} \) ✖️
- *Your response differs from the correct answer by more than 10%. Double check your calculations.*
- \( \theta = 225^\circ \) ✖️
- *The response you submitted has the wrong sign.*
**(d) Find the polar coordinates of the points with Cartesian coordinates \((3x, -3y)\).**
- \( r = 4.24 \, \text{cm} \) ✖️
- *Your response differs from the correct answer by more than 10%. Double check your calculations.*
- \( \theta = 45^\circ \) ✖️
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