3 MOTION IN 3 DIMENSIONS 3.9 Motion with constant velocity
The corresponding components of the body’s velocity are then simply
dx
vx =vy =vz == cos t, (3.26)
dt
dy
= − sin t, (3.27)
dt
dz
= 3, (3.28)
dtwhilst the components of the body’s acceleration are given by
a =dvx
x dt
a =dvy= − sin t, (3.29)
= − cos t, (3.30)
y dta =dvz
z dt= 0. (3.31)1.22 Motion with constant velocity
An object moving in 3 dimensions with constant velocity v possesses a vector
displacement of the form
r(t) = r 0 + v t, (3.32)where the constant vector r 0 is the displacement at time t = 0. Note that dr/dt =
v and d^2 r/dt^2 = 0 , as expected. As illustrated in Fig. 14 , the object’s trajectory
is a straight-line which passes through point r 0 at time t = 0 and runs parallel to
vector v.
1.23 Motion with constant acceleration
An object moving in 3 dimensions with constant acceleration a possesses a vector
displacement of the form
r(t) = r 0 + v 0 t^ +^1
a t^2. (3.33)
2