Also, v(0) = 0 yields C = 1. Thus v(t) = 1 − cos t; and since cos t 1 for all t we
see that v(t) 0 for all t. Thus, the distance traveled is
B. MOTION ALONG A PLANE CURVE
BC ONLYIn Chapter 4, §K, it was pointed out that, if the motion of a particle P along a
curve is given parametrically by the equations x = x(t) and y = y(t), then at time t
the position vector R, the velocity vector v, and the acceleration vector a are:
The components in the horizontal and vertical directions of R, v, and a are
given, respectively, by the coordinates in the corresponding vector. The slope of
v is ; its magnitude,
is the speed of the particle, and the velocity vector is tangent to the path. The
slope of a is The distance the particle travels from time t 1 to t 2 is given
by
How integration may be used to solve problems of curvilinear motion is
illustrated in the following examples.
BC ONLY