1
Assignment
No. ( 3 ) : Kinematics of plane motion
Cartesian coordinates
1.
The parametric equations of the plane motion of a particle are :
x = 16t
,
y = 12t – 5t
2
where
x, y
are in meters and t is in seconds . Determine :
a–the time, the position and the velocity when the particle’s path intersects the
horizontal x–axis
b – the maximum height of the path above the horizontal x – axis and the
velocity of the
particle at the maximum height .
2.
The
parametric
equations
of
a
particle`
s
path
are
given
by
:
x = a cos
2
t
,
y = a sin
2
t
where a is constant .Determine :
a – the initial conditions .
b – the equation of the path .
cthe acceleration of
the particle at the points of zero velocity
.
3.
The Cartesian equation of the path of a particle is given by :
x
8
y
2
=
,
where
x,y
are
in
meters
.
The
initial
conditions
of
the
motion
are
)
0
,
0
(
)
y
,
x
(
,
)
4
,
2
(
)
y
,
x
(
o
o
0
0
=
=
and the
y
– component of acceleration is
y
4
y
−
=
m/s
2
. Determine :
a – the parametric equations of the path.
b – the time interval between two successive positions of zero velocity.
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 Spring '08
 elbarki
 Acceleration, Particle, Euclidean geometry, Parametric equation

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