Page 176 - Introduction to Continuum Mechanics

Kinematics of a Continuum 161

(a) For this motion, repeat part (a) of the previous problem.

(b) Find the velocity and acceleration as a function of time of a particle that is initially at the
origin.
(c)Find the velocity and acceleration as a function of time of the particles that are passing
through the origin.
g
3.5. The position at time t of a particle initially at (A^^t^s) i given by

(a) Sketch the deformed shape, at time t = I of the material line OA which was a straight line
at t = 0 with O at (0,0,0) and ,4 at (0,1,0).
(b) Find the velocity at t = 2, of the particle which is at (1,3,1) au = 0.
(c) Find the velocity of a particle which is at (1,3,1) at t = 2.

3.6, The position at time t of a particle initially at (Xi^2^3)»is given by

(a) Find the velocity at t — 2 for the particle which was at (1,1,0) at the reference time.
(b) Find the velocity at t = 2 for the particle which is at the position (1,1,0) at t — 2.
3.7. Consider the motion

(a) Show that reference time is t = t 0.

(b) Find the velocity field in spatial coordinates.
(c) Show that the velocity field is identical to that of the following motion

3.8. The position at time t of a particle initially at (XiJC^JCs) is given by

(a) For the particle which was initially at (1,1,0), what are its positions in the following instants
of time: t - 0, t = 1, t = 2.
(b) Find the initial position for a particle which is at (1,3,2) at t = 2.
(c) Find the acceleration at t = 2 of the particle which was initially at (1,3,2).

(d) Find the acceleration of a particle which is at (1,3,2) at t = 2.
3.9. (a)Show that the velocity field