Question

A 3.00-kg particle starts from the origin at time zero. Its velocity as a function of time is given by v = (3t^2) i+ (2t) j where v is in meters per second and t is in seconds.

(a) Find its position at t = 1s.

(b) What is its acceleration at t = 1s ?

(c) What is the net force exerted on the particle at t = 1s ?

(d) What is the net torque about the origin exerted on the particle at t = 1s ?

(e) What is the angular momentum of the particle at t = 1s ?

(f) What is the kinetic energy of the particle at t = 1s ?

(g) What is the power injected into the system of the particle at t = 1s ?

please answer them all together since they are related to each other

Answer #1

A 14.00 kg particle starts from the origin at time zero. Its
velocity as a function of time is given by v with arrow = 9t2î +
4tĵ where v with arrow 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.
r =________
(c) Find its acceleration as a function of time.
a=_______m/s^2 (
(d) Find the net force exerted on the particle as...

A particle of mass 2.00 kg moves with position r(t) = x(t) i +
y(t) j where x(t) = 10t2 and y(t) = -3t + 2, with x and y in meters
and t in seconds.
(a) Find the momentum of the particle at time t = 1.00 s.
(b) Find the angular momentum about the origin at time t = 3.00
s.

A) A particle starts from the origin with velocity 5 ?̂m/s at t
= 0 and moves in the xy plane with a varying acceleration given by
?⃗ = (2? ?̂+ 6√? ?̂), where ?⃗ is in meters per second squared and
t is in seconds.
i) Determine the velocity of the particle as a function of
time.
ii) Determine the position of the particle as a function of
time.
(Explanation please )

A particle starts from the origin with velocity 5 ?̂m/s at t = 0
and moves in the xy plane with a varying acceleration given by ?⃗ =
(2? ?̂+ 6√? ?̂), where ?⃗ is in meters per second squared and t is
in seconds. i) Determine the VELOCITY and the POSITION of the
particle as a function of time.

A particle starts at the origin with initial velocity ⃗v(0) = ⃗i
− ⃗j + ⃗k. Its acceleration is ⃗a(t) = 4t⃗i + 3t⃗j − ⃗k. Find its
position at t = 3.

The position vector of a particle of mass 2kg is given as a
function of time by:
r = (4i + 2t j + 0k) m, when t is given in
seconds.
(a) Determine the angular momentum of the particle as a function
of time.
(b) If the object was a sphere of radius 5 cm, what would be its
rotational frequency?

At time t, r→ = 8.60t2
î - (4.90t + 6.10t2) ĵ gives the
position of a 3.0 kg particle relative to the origin of an
xy coordinate system ( r→ is in meters and t is
in seconds). (a) Find the torque acting on the
particle relative to the origin at the moment 4.50 s
(b) Is the magnitude of the particle’s angular
momentum relative to the origin increasing, decreasing, or
unchanging?

At time t, r→ = 1.70t2
î - (7.60t + 7.80t2) ĵ gives the
position of a 3.0 kg particle relative to the origin of an
xycoordinate system ( r→ is in meters and t is in
seconds). (a) Find the torque acting on the
particle relative to the origin at the moment 6.50 s
(b) Is the magnitude of the particle’s angular
momentum relative to the origin increasing, decreasing, or
unchanging?

A particle is to move in an xy plane, clockwise around
the origin as seen from the positive side of the z axis.
In unit-vector notation, what torque acts on the particle at time
t = 7.6 s if the magnitude of its angular momentum about
the origin is (a)8.4 kg·m2/s,
(b)8.4t2
kg·m2/s3,
(c)8.4t1/2
kg·m2/s3/2, and
(d)8.4/t2
kg·m2*s?

A moving particle starts at an initial position
r(0) = <1, 0, 0> with initial velocity
v(0) = i - j +
k. Its acceleration is a(t) = 4t
i + 4t j +
k.
Find its velocity, v(t), and position,
r(t), at time t.

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