A particle moves in a straight line along the x-axis. Its displacement is given by the formulas(t) = t2 − 4t2 + 7t. If displacement is in meters and time is in seconds, find: a.) The average velocity over the time interval [4,7]b.) The instantaneous velocity at t = 4.c.) The rate of change of velocity at t = 5.
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 line along the x-axis. Its displacement is given by the formula
s(t) = t2 − 4t2 + 7t. If displacement is in meters and time is in seconds, find:
a.) The average velocity over the time interval [4,7]
b.) The instantaneous velocity at t = 4.
c.) The rate of change of velocity at t = 5.
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