Arc Length and Speed on Parametric and Polar Curves Worksheet with Answer Key

What's on the worksheet

1. Find the speed dsdt as a simplified function of t.
   x = e^t\cos t, y = e^t\sin tx = t - \sin t\cos t, y = \sin^2 tx = 3\cos t + 4\sin t, y = 4\cos t - 3\sin t
2. A garden snail crawls across a flat paving stone and leaves a shiny trail.
3. Find the speed dsdt of the curve x = 10t³, y = 3t^5 - 15t, and the length of the curve for 0 ≤ t ≤ 2.
4. Find the length of the spiral r = 2θ² for 0 ≤ θ ≤ 3 √(5).
5. A circle of radius 3 rolls without slipping along the x-axis.
6. x y -4 3 -3 The curve x = 4 t, y = 3 2t, 0 ≤ t ≤ 2π, is the figure eight shown, which crosses itself at the origin.