Coordinates) of a particle is given by the function r(t) = ( (1/3) cos t^3 , (1/3) sin t^3 ) m where time is measured in seconds. Based on this information, answer the questions below. a) What is the radius of the circle that the particle moves along? b) What is the velocity of the particle as a function of time? c) What is the speed of the particle as a function of time? d) At time t = 2 sec, what is the acceleration of the particle in tangentia
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.
The position vector (in Cartesian Coordinates) of a particle is given by the function r(t) = ( (1/3) cos t^3 , (1/3) sin t^3 ) m where time is measured in seconds. Based on this information, answer the questions below.
a) What is the radius of the circle that the particle moves along?
b) What is the velocity of the particle as a function of time?
c) What is the speed of the particle as a function of time?
d) At time t = 2 sec, what is the acceleration of the particle in tangential and normal components?
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