Position, velocity, and acceleration Suppose the position of anobject moving horizontally along a line after t seconds is given by thefollowing functions s = ƒ(t), where s is measured in feet, with s > 0corresponding to positions right of the origin.a. Graph the position function.b. Find and graph the velocity function. When is the object stationary,moving to the right, and moving to the left?c. Determine the velocity and acceleration of the object at t = 1.d. Determine the acceleration of the object when its velocity is zero.e. On what intervals is the speed increasing?17. ƒ(t) = 2t2 - 9t + 12; 0 ≤ t ≤ 3
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.
Position, velocity, and acceleration Suppose the position of an
object moving horizontally along a line after t seconds is given by the
following functions s = ƒ(t), where s is measured in feet, with s > 0
corresponding to positions right of the origin.
a. Graph the position function.
b. Find and graph the velocity function. When is the object stationary,
moving to the right, and moving to the left?
c. Determine the velocity and acceleration of the object at t = 1.
d. Determine the acceleration of the object when its velocity is zero.
e. On what intervals is the speed increasing?17. ƒ(t) = 2t2 - 9t + 12; 0 ≤ t ≤ 3
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