Question

When at the origin (0,0) the initial velocity of a particle is ?⃗0 = (2.0?̂ + 5.0?̂) ? / ? and its constant acceleration is ?⃗ = (7.0?̂ + 5.0?̂) ? / ? two . Find the final position of the particle when its velocity is ?⃗ = (16.0?̂ + 15.0?̂) ? / ?. (First find the time it takes to reach your position final).

Answer #1

Given data:

at origin (0,0) velocity of particle is

moving with constant acceleration of

and final velocity

Now from equation of motion,

Now Final position of particle is

s = Final position of particle.

Now as s_{o} = (0,0)

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.

A particle moves in the xy plane, starting from the origin at
t=0 with an initial velocity having an x-component of 6 m/s and y
component of 5 m/s. The particle experiences an acceleration in the
x-direction, given by ax=4t m/s2. Determine the acceleration vector
at any later time. Determine the total velocity vector at any later
time Calculate the velocity and speed of the particle at t=5.0 s,
and the angle the velocity vector makes with the x-axis. Determine...

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.

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.

Find the velocity and position vectors of a particle that has
the given acceleration and the given initial velocity and
position.
a(t) = 4t, et, e−t v(0) =
0,0,−5 r(0) = 0,1, 4

please ASAP!!
Suppose that a particle has the following acceleration vector
and initial velocity and position vectors.
a(t) = 5 i +
9t k,
v(0) = 3 i
−
j, r(0)
= j + 6 k
(a)
Find the velocity of the particle at time t.
(b)
Find the position of the particle at time t.

A particle is launched from the origin along the
x-axis at an initial velocity of 2 m/s. If the particle is
accelerated according to the formula a(t) = -sin(t) where t is in
seconds, what is the particle's position at time t = pi
seconds?

Find the position vector of a particle that has acceleration
2i+4tj+3t^2k, initial velocity v(0)=j+k and initial position
r(0)=j+k

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 +
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(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...

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