Question

The acceleration of a particle that moves linearly is given as ? = - (0.1 + sin (? / 0.75)). The unit of acceleration is m / s2 and the unit of s is m. In t seconds, when s = 0, b and v = 0.98 values are as in the table. Calculate the velocity of the particle when (i) s = -1 m, (ii) the position of the particle when the velocity is maximum (iii) the maximum velocity that the particle has reached.

Answer #1

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The acceleration of a linear moving particle is given as ? = -
(0.1 + sin (? / ?)).
m / s2
and the unit of s is m. In t seconds, when s = 0, b= 3.5 and v =
0.95 values are as in the table.
(I)When s = -1 m, the speed of the particle,
(ii) the position of the particle when the speed is the
maximum,
(iii) the particle
Calculate the maximum speed it has reached.

A particle moves according to a law of motion
s = f(t),
t ≥ 0,
where t is measured in seconds and s in feet.
(If an answer does not exist, enter DNE.)
f(t) = t3 − 8t2 + 23t
(a) Find the velocity at time t.
v(t) = ft/s
(b) What is the velocity after 1 second?
v(1) = ft/s
(c) When is the particle at rest?
(d) When is the particle moving in the positive direction? (Enter
your...

A particle moves according to a law of motion s = f(t), t ≥ 0,
where t is measured in seconds and s in feet. (If an answer does
not exist, enter DNE.) f(t) = t3 − 8t2 + 27t (a) Find the velocity
at time t. v(t) = ft/s (b) What is the velocity after 1 second?
v(1) = ft/s (c) When is the particle at rest? (d) When is the
particle moving in the positive direction? (Enter your...

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 moves along one dimension with a constant
acceleration of 4.60 m/s2 over a time interval. At the end of this
interval it has reached a velocity of 13.8 m/s.
(a)
If its original velocity is 6.90 m/s, what is its displacement
(in m) during the time interval?
m
(b)
What is the distance it travels (in m) during this
interval?
m
(c)
A second particle moves in one dimension, also with a constant
acceleration of 4.60 m/s2 ,...

The acceleration of a particle moving only on a horizontal
xy plane is given by a→=3ti^+4tj^, where a→ is in meters
per second-squared and t is in seconds. At t = 0,
the position vector r→=(19.0m)i^+(44.0m)j^ locates the particle,
which then has the velocity vector v→=(5.40m/s)i^+(1.70m/s)j^. At
t = 4.10 s, what are (a) its position
vector in unit-vector notation and (b) the angle
between its direction of travel and the positive direction of the
x axis?

A particle has a constant acceleration of a =
axi +
ayj and at t
= 0 it is at rest at the origin
What is the particle’s position as a function of time?
What is the particle’s velocity as a function of time?
What is the particle’s path, expressed as y as a
function of x?
The position of a particle is given by r =
(at2)i +
(bt3)j +
(ct-2)k, where a,
b, and c are constants.
What...

A particle is moving along a straight line and has acceleration
given by a(t) = 20t^3+12t^2}. Its initial velocity is v( 0 ) = 4 m
/ s and its initial displacement is s( 0 ) = 5 m. Find the position
of the particle at t = 1 seconds.

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 moves along the x axis. It is initially at the
position 0.150 m, moving with velocity 0.080 m/s and acceleration
-0.340 m/s2. Suppose it moves with constant acceleration for 5.60
s. (a) Find the position of the particle after this time. (b) Find
its velocity at the end of this time interval. Next, assume it
moves with simple harmonic motion for 5.60 s and x = 0 is its
equilibrium position. (Assume that the velocity and acceleration is...

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