APFIVE Properties of Parametrically Defined Motion
A particle moves in the plane such that its position at time $$t$$ is given by $$x(t)=t^2-3*t$$ and $$y(t)=2*t+1$$. All of the following statements about the particle’s motion are true EXCEPT:
A
The particle reaches a horizontal extremum at $$t=0$$.
B
Differentiating $$x(t)$$ and $$y(t)$$ with respect to $$t$$ provides the components of the particle’s velocity vector.
C
The vertical motion, described by $$y(t)=2*t+1$$, is linear, implying a constant vertical velocity.
D
The horizontal motion, given by $$x(t)=t^2-3*t$$, is quadratic and its vertex represents the horizontal extremum.
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