Question

**“A butterfly flies along with a velocity vector given by
v = (a-bt²) Î + (ct) ĵ where a=1.4 m/s, b=6.2 m/s³, and c=2.2 m/s².
When t= 0 seconds, the butterfly is located at the origin.
Calculate the butterfly’s position vector and acceleration vector
as functions of time. What is the y-coordinate as it flies over x =
0 meters after t = 0 seconds?”**

Answer #1

the position of an object in one dimension is given by
X(t)=A+Bt+Ct^2, where x is in meters and t is in seconds. find the
velocity and acceleration at 3 seconds. what are the units for A,
B, and C?

A particles velocity along the x-axis is described by v(t) = At
+ Bt^2, where t is in seconds, velocity is in m/s^2, A = 1.18m/s^2
and B = -0.61m/s^3. What is the distance traveled, in m, by the
particle between times t0=1.0 and t1=3.0? please show steps and
calculations

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 ?

Suppose that the position vector for a particle is given as a
function of time by vector r (t) = x(t)î + y(t)ĵ, with x(t) = at +
b and y(t) = ct2 + d, where a = 1.90 m/s, b = 1.10 m, c = 0.128
m/s2, and d = 1.12 m.
(a) Calculate the average velocity during the time interval from
t = 2.05 s to t = 3.75 s. vector v = m/s
(b) Determine the 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...

A proton moves through a region containing a uniform electric
field given by = 44.0 ĵ V/m and a
uniform magnetic field = (0.200 î +
0.300 ĵ + 0.400 ) T. Determine the acceleration of
the proton when it has a velocity = 230
î m/s.

A proton moves through a region containing a uniform electric
field given by = 70.0 ĵ V/m and a
uniform magnetic field = (0.200 î +
0.300 ĵ + 0.400 ) T. Determine the acceleration of
the proton when it has a velocity = 250
î m/s.

A proton moves through a region containing a uniform electric
field given by = 44.0 ĵ V/m and a
uniform magnetic field = (0.200 î +
0.300 ĵ + 0.400 ) T. Determine the acceleration of
the proton when it has a velocity = 230
î m/s.

A particle's velocity along the x-axis is described by v(t)= At
+ Bt2, where t is in seconds, v is in m/s,
A= 0.85 m/s2, and B= -0.69 m/s3.
Acceleration= -0.53 m/s2 @ t=0 and the Displacement=
-2.58 m b/w t=1s to t=3s.
What is the distance traveled in meters, by the particle b/w
times t=1s and t=3s?

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.

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