n a particular Cartesian coordinate system, a particle has coordinates x(t) = 2sin(3t) + C, y = 0, z = 0, where t is in seconds, x is in meters, and C is a constant to be determined by the data. At t = 0 the particle was at x = 1 m. Part (a) Find the value of constant C, in meters. Part (b) Find the instantaneous velocity, in meters per second, at t = 1.5 s. Part (c) Find the instantaneous velocity, in meters per second, at t = 1.5 s.
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.
n a particular Cartesian coordinate system, a particle has coordinates
x(t) = 2sin(3t) + C,
y = 0,
z = 0,
where t is in seconds, x is in meters, and C is a constant to be determined by the data. At t = 0 the particle was at x = 1 m.
Part (a) Find the value of constant C, in meters.
Part (b) Find the instantaneous velocity, in meters per second, at t = 1.5 s.
Part (c) Find the instantaneous velocity, in meters per second, at t = 1.5 s.
Part (d) Find the instantaneous velocity, in meters per second, at t = 2.8 s.
Part (e) Find the instantaneous acceleration, in meters per square second, at t = 1.5 s.
Part (f) Find the instantaneous acceleration, in meters per square second, at t = 1.5 s.
14% Part (g) Find the instantaneous acceleration, in meters per square second, at t = 2.8 s.
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