Parametric Equations - Velocity and Acceleration Practice Problems Online

Suppose the position of point $P=(x(t), y(t))$ at time $t$ is given by $\left ( 5{t}^2+4, -5{t}^3+4t \right ) .$ What is the magnitude of acceleration of $P$ at time $t=5 ?$

{10}\sqrt{226}

{10}\sqrt{222}

{12}\sqrt{222}

{12}\sqrt{226}

Suppose the position of point $P=(x, y)$ at time $t$ is given by $\left ( 2t, -2{t}^2+4t \right ).$ What is the magnitude of the velocity of $P$ at time $t=8 ?$

{2}\sqrt{201}

{2}\sqrt{197}

{4}\sqrt{201}

{4}\sqrt{197}

Suppose the position of a particle $P$ at time $t$ is given by $\left ( -8{e}^t\cos t + 2 , 8{e}^t\sin t + 6 \right ).$ What is the angle $\alpha$ ( $0 < \alpha < \pi$ ) between the $x$ -axis and the velocity vector $\vec{v}$ of $P$ at time $t= \frac{\pi}{2}?$

\displaystyle{\frac{\pi}{4}}

\displaystyle{\frac{\pi}{2}}

\displaystyle{\frac{\pi}{3}}

\displaystyle{\frac{2\pi}{3}}

Leaving from the origin at the same time, point $P$ moves at a rate of $5$ cm per second in the positive direction of the $x$ -axis, while point $Q$ moves at a rate of $10$ cm per second in the positive direction of the $y$ -axis. What is the velocity vector $\vec{v}=\left ( \frac{dx}{dt} , \frac{dy}{dt} \right )$ of the intersection point between the line $\overline {PQ}$ and the line $y=3x$ ?

\displaystyle{({8},{4})}

\displaystyle{({4},{8})}

\displaystyle{({2},{6})}

\displaystyle{({6},{2})}

Suppose the position of point $P=(x(t), y(t))$ at time $t$ is given by $\left ( 4t-10\sin t, 10\cos t + 10 \right ) .$ What is the maximum speed attained by point $P?$

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Parametric Equations - Velocity and Acceleration

Parame演算tric Equations

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Parametric Equations - Velocity and Acceleration