Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = 3sin^2(t), y = 3cos^2(t), 0 ≤ t ≤ 3𝜋
Added by Joshua T.
Step 1
The velocity vector is given by the derivatives of x and y with respect to t: vx = dx/dt = d(3sin^2(t))/dt = 6sin(t)cos(t) vy = dy/dt = d(3cos^2(t))/dt = -6cos(t)sin(t) Show more…
Show all steps
Close
Your feedback will help us improve your experience
Wen Zheng and 92 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the distance traveled by a particle with position $(x, y) \quad$ as $t$ varies in the given time interval: $$x=\sin ^{2} t, \quad y=\cos ^{2} t, \quad 0 \leq t \leq 3 \pi$$
Parametric Equations and Polar Coordinates
Calculus of Parametric Curves
A particle moves on a vertical line so that its coordinates attime t isy = t^3 12t + 3; t 0. Find the distance theparticle travels over the time interval 0 < t < 4.
Audrey F.
Madhur L.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD