A particle moves in a straight path with the following acceleration as a function of velocity: a(t) = -k*v(t). At t0 = 0, the particle has an initial position x0 = 0 and an initial velocity of v0 > 0. Express the following functions in algebraic form: a) The equation for v(t) b) The equation for x(t) c) The equation for v(x) d) Skip? The equation for a(x) e) Draw the diagrams for these motion curves, roughly to a chosen scale f) Can you think of an alternate way to answer/confirm your answersfor c) and d)?
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 in a straight path with the following acceleration as a function of velocity: a(t) = -k*v(t).
At t0 = 0, the particle has an initial position x0 = 0 and an initial velocity of v0 > 0.
Express the following functions in algebraic form:
a) The equation for v(t)
b) The equation for x(t)
c) The equation for v(x)
d) Skip? The equation for a(x)
e) Draw the diagrams for these motion curves, roughly to a chosen scale
f) Can you think of an alternate way to answer/confirm your answersfor c) and d)?
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