1. A particle moves in the x- y plane with a time-dependent position vector given by: r(t) = (At)ê + (Bt − Ct²)ŷ where A = 10 m/s, B = 20 m/s, and C = 5 m/s². (a) Calculate (t) and a(t). (b) Does this particle have constant acceleration? (c) Does this particle's motion have a turning point in the x and/or y dimensions? If so, at what time(s) do these turning points occur?
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.
Please answer the questions using the variables provided and provide explanations and show work.
![**Problem:**
A particle moves in the \(x-y\) plane with a time-dependent position vector given by:
\[
\vec{r}(t) = (At)\hat{x} + (Bt - Ct^2)\hat{y}
\]
where \(A = 10 \, \text{m/s}\), \(B = 20 \, \text{m/s}\), and \(C = 5 \, \text{m/s}^2\).
(a) Calculate \(\vec{v}(t)\) and \(\vec{a}(t)\).
(b) Does this particle have constant acceleration?
(c) Does this particle's motion have a turning point in the \(x\) and/or \(y\) dimensions? If so, at what time(s) do these turning points occur?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4143f45a-5c96-4449-af2f-abda697f3e91%2F5901fc86-4cb3-4bc2-a365-0587a57e9d73%2F7lkexi_processed.jpeg&w=3840&q=75)
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