If … for travel up the line …, draw a triangle to…

The ${\mathbf{u}}_{\theta }$ component of acceleration is ____ $=0$ for a central force, which is in the direction of ____. Then $r^{2}d\theta /dt$ is constant (new proof) because its derivative is $r$ times ____.

If $r^{2}d\theta /dt=2$ for travel up the line $x=1$, draw a triangle to show that $r=\sec \theta$ and integrate to find the time to reach $(1,1)$.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §12.4 Polar Coordinates and Planetary Motion, #10