6. 6
Curvilinear Motion: Position, Velocity & Acceleration
• Position vector of a particle at time t is defined by a
vector between origin O of a fixed reference frame and
the position occupied by particle.
• Consider particle which occupies position P defined
by at time t and P’ defined by at t + Dt,r
r
D
D
D
D
D
D
dt
ds
t
s
v
dt
rd
t
r
v
t
t
0
0
lim
lim
instantaneous velocity (vector)
instantaneous speed (scalar)
Velocity is tangent to path
7. 7
Curvilinear Motion: Position, Velocity & Acceleration
D
D
D dt
vd
t
v
a
t
0
lim
instantaneous acceleration (vector)
• Consider velocity of particle at time t and velocity
at t + Dt,
v
v
• In general, acceleration vector is not tangent to
particle path and velocity vector.
15. Example(1)
At any instant the horizontal position of the
weather balloon in below Fig is defined by
x = (8t) ft, where (t) is in seconds. If the
equation of the path is y = x2/10, determine
the magnitude and direction of the velocity
and the acceleration when t = 2 s.
8/5/2013 mohammed.abdelgadir1983@gmail.com 15
22. Example (2)
For a short time, the path of the plane in below
Fig. is described by Y = (0.001X2) m. If the
plane is rising with a constant velocity of
10m/s , determine the magnitudes of the
velocity and acceleration of the plane when it
is at y = 100 m.
8/5/2013 mohammed.abdelgadir1983@gmail.com 22
