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 of unit mass is projected vertically upwards in a medium whose resistance is given by R=-kv2 where v is its velocity. Its initial velocity is u.
a) Using Newton’s 2nd Law and write out the equation of motion as a differential equation in terms of velocity and displacement. You must include an FBD as part of the solution.
b) Prove that its velocity after rising through a distance s satisfies (first picture)
c)Using part(b) show that when the particle reaches a maximum height h, then (second picture)
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