The car in the preceding problem travels at constant speed and completes one lap in $55 \mathrm{~s}$. Assume the same starting point $(250 \mathrm{~m}, 0)$. Find (c) its instantaneous velocity at the end of one lap.

A circular racetrack with $250 \mathrm{~m}$ radius lies in the $x-y$ plane and is centered at the origin. A car rounds the track counterclockwise starting at the point $(250 \mathrm{~m}, 0)$. Find the total distance traveled and the displacement after (b) one-half lap.

A circular racetrack with $250 \mathrm{~m}$ radius lies in the $x-y$ plane and is centered at the origin. A car rounds the track counterclockwise starting at the point $(250 \mathrm{~m}, 0)$. Find the total distance traveled and the displacement after (a) one-quarter lap.

A roller coaster goes $26 \mathrm{~m}$ along a section of track sloping $10^{\circ}$ below the horizontal, followed by a $15-\mathrm{m}$ section sloping upward at $6^{\circ}$, followed by an 18-m section of level track. Find the net displacement.

You drive due east at $85 \mathrm{~km} / \mathrm{h}$ for $50 \mathrm{~min}$. Then you follow a road going $60^{\circ}$ south of east, going $90 \mathrm{~km} / \mathrm{h}$ for another 30 min. Find your total displacement.

Add the following vectors, first graphically, then using components: $\vec{R}$ has magnitude $6.0 \mathrm{~m}$ and points in the $+x$-direction, and $\vec{S}$ has a magnitude $9.0 \mathrm{~m}$ and direction angle $60^{\circ}$.