A 18.00 kg particle starts from the origin at time zero. Its velocity as a function of time is given by
= 7t2î + 3tĵ
where is in meters per second and t is in seconds. (Use the following as necessary: t.)
(a) Find its position as a function of time.
=
b) Describe its motion qualitatively.
This answer has not been graded yet.
(c) Find its acceleration as a function of time.
=
m/s2
(d) Find the net force exerted on the particle as a function of
time.
=
N
(e) Find the net torque about the origin exerted on the particle as
a function of time.
τ =
N · m
(f) Find the angular momentum of the particle as a function of
time.
=
kg · m2/s
(g) Find the kinetic energy of the particle as a function of
time.
K =
J
(h) Find the power injected into the particle as a function of
time.
P =
W
given
m = 18 kg
v = 7 t2 î + 3 t ĵ
a )
x = v.dt
= ( 7 t2 î + 3 t ĵ ) . dt
= 7 ( t3 / 3 ) i + 3 ( t2 / 2 ) j
x = ( 2.33 t3 i + 1.5 t2 j ) m
b )
to describe its motion that
if the vectors x and v parallel to each of them then the motion of the particle obviously in straight line,
but this is based on the vectors.
c )
acceleration = rate of change of velocity with respect to time
a = dv / dt
= d ( 7 t2 î + 3 t ĵ ) / dt
= 7 x 2 t i + 3 j
a = ( 14 t i + 3 j ) m/sec2
d )
the net force exerted on the particle as a function of time " F "
F = m a
= 18 x ( 14 t i + 3 j )
F = ( 252 t i + 54 j ) N
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