Question

1-The velocity of a particle is v = { 6 **i** + (
28 - 2 t ) **j** } m/s, where t is in seconds. If r=0
when t=0, determine particle displacement during time interval t =
3 s to t = 8 s in the y direction.

2-A particle, originally at rest and located at point (1 ft, 4
ft, 5 ft), is subjected to an acceleration of a={ 3 t
**i** + 17 t^{2}**k**} ft/s.
Determine magnitude of the particle’s position at t = 1 s.

3-The velocity of a particle is given by v = { 14t^{2}
**i** + 3t^{3}**j** + (8t+4)
**k** } m/s, where t is in seconds. If the particle is
at the origin when t=0s, determine magnitude of particle’s
acceleration when t=7s.

4-A rocket is fired from rest at x=0 and travels along a
parabolic trajectory described by y^{2} = { 180
(10^{3}) x } m. If the x component of acceleration is
a_{x} = t^{2}/7, where t is in seconds, determine
the magnitude of the rocket’s velocity when t = 5 s.

please help

Answer #1

Practice Derivatives and integrals. A particle’s velocity is
described by the function v = ( t^2 – 7t + 10) m/s, where t is in
s.
a) Graph the velocity function for t in the interval 0s-6s.
b) At what times does the particle reach its turning points?
c) Find and graph the position function x (t).
d) Find and graph the acceleration function a(t).
e) What is the particle’s acceleration at each of the turning
points?

A particle travels along the path defined by the parabola
y=0.2x^2. If the component of velocity along t he x axis is
Vx=(2.9t)ft/s, where t is in seconds. determine the magnitude of
the particle's acceleration when t = 1s. when t = 0 , x =0 and y =
0.

) A particle is moving according to the velocity equation v(t) =
9t^2-8t-2 . The equation uses units of meters and seconds
appropriately. At t = 1 s the particle is located at x = 2 m. (a)
What is the particle's position at t = 2 s? (b) What is the
particle's acceleration at t = 1 s? (c) What is the particle's
average velocity from t = 2 s to t = 3 s?

The velocity of a particle is v = { 5 i + ( 6 – 2t ) j } m/sec ,
where ‘ t ‘ is in secs. r = 0, When t = 0 , determine the
displacement of the particle during the time interval t = 1 secs to
t = 3secs .

The x and y components of the velocity of a particle are
Vx=(2t + 4)ft/s &
Vy=(8/y)ft/s. Initially, the particle if found at
coordinates x=1 and y=0.
Determine the position, magnitude of velocity, and magnitude of
the acceleration of the particle when t = 2s

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...

The components ? and ? of the velocity of a particle are:
?? = (2 ? + 4) f / s ?? = (8 ⁄ ?) f / s (feet/sec)
Initially the particle is in the coordinates ? = 1 and ? = 0.
Determine the position, magnitude of velocity, and magnitude of
acceleration of the
particle when t = 2 s.

A particle travels along a straight line with a velocity
v=(12−3t^2) m/s , where t is in seconds. When t = 1 s, the particle
is located 10 m to the left of the origin.
Determine the displacement from t = 0 to t = 7 s.
Determine the distance the particle travels during the time
period given in previous part.

The velocity v of a particle moving in the
xy plane is given by
v = (7.0t
-4.0t2 )i +
7.5j, in m/s. Here v is
in m/s and t (for positive time) is in s. What is
the acceleration when t = 3.0 s?
i-component of acceleration?
j-component of acceleration?
When (if ever) is the acceleration zero (enter time in
s or 'never')?
When (if ever) is the velocity zero (enter time in s or
'never')?

A particle moves according to a law of motion
s = f(t),
t ≥ 0,
where t is measured in seconds and s in
feet.
f(t) =
t3 − 9t2
+ 15t
(a) Find the velocity at time t.
v(t) =
(b) What is the velocity after 4 s?
v(4) = ft/s
(c) When is the particle at rest?
t = s (smaller value)
t = s (larger value)
(d) When is the particle moving in the positive direction? (Enter
your answer...

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