AP Calculus BC / Parametric Equations, Polar Coordinates, and Vector-Valued Functions / Question No. 33

33. For any time \( t \ge 0 \), if the position of a particle in the \(xy\)-plane is given by \( x=e^t \) and \( y=e^{-t} \), then the speed of the particle at time \( t=1 \) is

2.693

2.743

3.086

3.844

Answer is: option2

2.743

Solution:

\( p(t)=\langle e^t, e^{-t} \rangle \)

\( v(t)=\langle e^t, -e^{-t} \rangle \)

\( v(1)=\left\langle e, -\dfrac{1}{e} \right\rangle \)

The speed at \( t=1 \) is \( |v(1)|=\sqrt{e^2+\dfrac{1}{e^2}} \approx 2.743 \)

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Home Practice Questions AP Calculus BC Parametric Equations, Polar Coordinates, and Vector-Valued Functions Question No. 33

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