A particle moves with position r(t) = x(t) i + y(t) j where x(t) = 10t2 and y(t) = -3t + 2, with x and y in meters and t in seconds. (a) Find the average velocity for the time interval from 1.00 s to 3.00 s. (b) Find the instantaneous velocity at t = 1.00 s. (c) Find the average acceleration from 1.00 s to 3.00 s. (d) Find the instantaneous acceleration at t = 1.00 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.
A particle moves with position r(t) = x(t) i + y(t) j where x(t) = 10t2 and y(t) = -3t + 2, with x and y in meters and t in seconds.
(a) Find the average velocity for the time interval from 1.00 s to 3.00 s.
(b) Find the instantaneous velocity at t = 1.00 s.
(c) Find the average acceleration from 1.00 s to 3.00 s.
(d) Find the instantaneous acceleration at t = 1.00 s.
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