James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

Chapter 13
Concept Check Answers (continued)
8. (a) How do you find the velocity, speed, and acceleration of a
particle that moves along a space curve?
If rstd is the position vector of the particle on the space
curve, the velocity vector is vstd − r9std, the speed is given
by | vstd | , and the acceleration is astd − v9std − r0std.
(b) Write the acceleration in terms of its tangential and normal
components.
a − a TT 1 a NN, where a T − v9 and a N − v 2 sv − | v | is
speed and is the curvature).
9. State Kepler’s Laws.
■ A planet revolves around the sun in an elliptical orbit with
the sun at one focus.
■ The line joining the sun to a planet sweeps out equal areas
in equal times.
■ The square of the period of revolution of a planet is proportional
to the cube of the length of the major axis of its
orbit.
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