Question

Find the velocity and acceleration vectors for the parametric equations $x = 9 \cos(t^2)$, $y = 9 \sin(t^2)$, $z = t^2$. $\vec{v} = -9 \sin(2t) \vec{i} + 9 \sin(2t) \vec{j} + t^2 \vec{k}$ $\vec{a} = -18 \cos(2t) \vec{i} + 18 \cos(2t) \vec{j} + 2 \vec{k}$

          Find the velocity and acceleration vectors for the parametric
equations $x = 9 \cos(t^2)$, $y = 9 \sin(t^2)$, $z = t^2$.
$\vec{v} = -9 \sin(2t) \vec{i} + 9 \sin(2t) \vec{j} + t^2 \vec{k}$
$\vec{a} = -18 \cos(2t) \vec{i} + 18 \cos(2t) \vec{j} + 2 \vec{k}$

Find the velocity and acceleration vectors for the parametric
equations x = 9 cos(t^2), y = 9 sin(t^2), z = t^2.
v⃗ = -9 sin(2t) i⃗ + 9 sin(2t) j⃗ + t^2 k⃗
a⃗ = -18 cos(2t) i⃗ + 18 cos(2t) j⃗ + 2 k⃗

Added by Emily A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Qbs Educator

Step 1

Given: x = 9cos(t^2) y = 9sin(t^2) z = t^2 Taking the derivative of each component: dx/dt = -18tsin(t^2) dy/dt = 18tcos(t^2) dz/dt = 2t So, the velocity vector V is: V = -18tsin(t^2)i + 18tcos(t^2)j + 2tk Now, let's find the acceleration vector. To do this, we Show more…

Show all steps

Thanks for your feedback!

Please help me figure out the correct answers, everything is wrong except for the 2k. Find the velocity and acceleration vectors for the parametric equations x = 9cos(t^2), y = 9sin(t^2), z = t^2. V = -18tcos(t^2)i + 18tsin(t^2)j + 2tk A = (-36t^2sin(t^2) - 18cos(t^2))i + (36t^2cos(t^2) - 18sin(t^2))j + 2k