Context The position of a peculiar fish as a function of time is given by the following equation. Time is in seconds, position is in meters, and the positive direction is to the right. x(t) = 2t3 + 12t2 - 72t The fish's position, velocity, and acceleration functions are x = 2t3 + 12t2 - 72t, v = 6t2 + 24t - 72, and a = 12t + 24. Question: When, if ever, is the fish at rest? Drag the appropriate label(s) to the correct location(s) on the number line. Remember that it is the circle in the upper left corner of the label that must be in the correct place. Drag the period (.) to denote a single time; for example, t=0. Drag the left bracket ([) to denote the lower end of a range; for example, t>0. Drag the right bracket (]) to denote the upper end of a range; for example, t<0. Drag "none" anywhere near the line if the fish is never at rest. You may place as many of each symbol on the line as needed. See image attached:
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.
Context
The position of a peculiar fish as a function of time is given by the following equation. Time is in seconds, position is in meters, and the positive direction is to the right.
x(t) = 2t3 + 12t2 - 72t
The fish's position, velocity, and acceleration functions are x = 2t3 + 12t2 - 72t, v = 6t2 + 24t - 72, and a = 12t + 24.
Question:
When, if ever, is the fish at rest?
Drag the appropriate label(s) to the correct location(s) on the number line. Remember that it is the circle in the upper left corner of the label that must be in the correct place.
- Drag the period (.) to denote a single time; for example, t=0.
- Drag the left bracket ([) to denote the lower end of a range; for example, t>0.
- Drag the right bracket (]) to denote the upper end of a range; for example, t<0.
- Drag "none" anywhere near the line if the fish is never at rest.
You may place as many of each symbol on the line as needed.
The problem provides the position, velocity, and acceleration functions of a fish in terms of time. We are asked to determine when the fish is at rest.
To solve this problem, we need to understand the meaning of "at rest" for the fish. The fish is at rest when its velocity is zero, i.e., it is not moving. So, we need to find the values of time at which the velocity of the fish is zero.
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