Question

Problem 2 The position of a particle at time tis F()-cost+jsint +kr (a) Show that both the speed and magnitude of the acceleration are constant at all times (b) Show that the angle between the velocity and acceleration is time-independent. (c) Describe in a few words, albeit clearly, the motion of the particle, assuming F(0) 0. Suppose that 2+-sin(s) +cos(t) and ry-s-t 2.3 Fnd Fias a function of x, y, s, t. function of t 8

Answer 1

de dt de dt -cost个-Sint J

c)since the projection of r(t) is circualr and the z compoment of the velocity is constant the motion of the particle is helical with a constant pitch

5S-

8 so diltexemtiat .I 3(3-t) sint 21- 3Cs-t) 3 (s-t -sint

ノ廿 it )2. 부 2( s-t ) ss'-t(y @y -sint 3 2(s-t) sin JT y3