Question

) 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?

Answer #1

The velocity of a particle moving along the x-axis
varies with time according to
v(t) = A +
Bt−1,
where
A = 7 m/s,
B = 0.33 m,
and
1.0 s ≤ t ≤ 8.0 s.
Determine the acceleration (in m/s2) and position (in
m) of the particle at
t = 2.6 s
and
t = 5.6 s.
Assume that
x(t = 1 s) = 0.
t = 2.6 s
acceleration m/s2 position m
?
t = 5.6 s
acceleration m/s2
position m ?

The position of a particle moving with constant acceleration is
given by x(t) = 2t2 +
8t + 4 where x is in meters and t is in
seconds.
(a) Calculate the average velocity of this particle between
t = 6 seconds and t = 9 seconds.
(b) At what time during this interval is the average
velocity equal to the instantaneous velocity?

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 t2k} ft/s.
Determine magnitude...

The velocity of a particle moving along a line is a function of
time given by v(t)=81/(t2+9t+18). Find the
distance
that the particle has traveled after t=9 seconds if it started at
t=0 seconds.

The
position of a particle in rectilinear motion is given by:
x(t) = (t^3 - 9t^2 + 24t + 5)ft. with t in seconds.
plot the position, velocity, and acceleration in the first 10
seconds

The velocity-time graph of a particle moving along the x-axis is
shown. The particle has zero velocity at t = 0.00 s and reaches a
maximum velocity, vmax, after a total
elapsed time, ttotal. If the initial
position of the particle is x0 = 7.29 m, the
maximum velocity of the particle is
vmax = 11.3 m/s, and the total elapsed
time is ttotal = 25.0 s, what is the
particle's position at t = 16.7 s?
b. At t...

.The x and y components of the velocity of a particle are: vx =
(2 t + 4) p / s vy = (8 ⁄ y) p / s Initially, the particle is
located at the coordinates x = 1 and y = 0. Determine the position,
the magnitude of the velocity and the magnitude of the particle's
acceleration when t = 2 s.

2). A particle moving on the x-axis has a time-dependent
position (t) given by the equation x (t) = ct - bt^3. Where the
units of x are meters (m) and time t in seconds (s). (Hint: you
must get derivatives, you need graph paper)
(a) So that the position in x has units of meter which are the
units of the constants c and b?
Sic = 5yb = 1.Desdeti = 0satf = 3s.
(b) What is its displacement,...

1) The position of a particle moving along x direction is given
by: x=8t-3t2.What is the velocity of the particle at t=2
s and what is the acceleration?
2) A roller coaster car starts from rest and descends
h1= 40 m. The car has a mass of 75 kg. What is the speed
at 20m while going down the hill?

The
equation of motioj of a partucle is given by s(t)= t^3 -6t^2 +9t
where s is in meters and t is in seconds.
a) Find when the particle is moving in the negatuve
direction
b) Find when the particle is accelerating in the positive
direction

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