Question
In: Physics
The position vector F(t) of a moving particle at time t[s] is given by F(t)= e^t...
The position vector F(t) of a moving particle at time t[s] is given by F(t)= e^t sin(t)i-j+e^t cos(t)k a) Calculate the acceleration a(t). b) Find the distance traveled by the particle at time t = 3π/2, if the particle starts its motion at time t = π/2. c) Find the unit tangent vector of this particle at time t = 3π/2. d) Find the curvature of the path of this particle at time t = 3π/2.
Solutions
genius_generous answered 2 years agoRelated Solutions
A particle is moving with the given data. Find the position of the particle. a(t) =...
A particle is moving with the given data. Find the position of
the particle. a(t) = 11 sin(t) + 3 cos(t), s(0) = 0, s(2π) = 18
A particle is moving with the given data. Find the position of the particle. v(t) =...
A particle is moving with the given data. Find the position of
the particle. v(t) = sin(t) − cos(t), s(0) = 4
The vector position of a 3.70 g particle moving in the xy plane varies in time...
The vector position of a 3.70 g particle moving in the
xy plane varies in time according to
r1 = (3î +
3ĵ)t +
2ĵt2
where t is in seconds and
r
is in centimeters. At the same time, the vector position of a
5.80 g particle varies as
r2 = 3î −
2ît2 −
6ĵt.
(a)
Determine the vector position (in cm) of the center of mass of
the system at t = 2.90 s.
rcm =
cm
(b)...
The vector position of a 3.95 g particle moving in the xy plane varies in time...
The vector position of a 3.95 g particle moving in the
xy plane varies in time according to
r1 = (3î +
3ĵ)t +
2ĵt2
where t is in seconds and r is in
centimeters. At the same time, the vector position of a 5.70 g
particle varies as
r2 = 3î −
2ît2 −
6ĵt.
(a)Determine the vector position (in cm) of the center of mass
of the system at t = 2.90 s.
rcm = cm
(b)Determine the...
The vector position of a 3.90 g particle moving in the xy plane varies in time...
The vector position of a 3.90 g particle moving in the xy plane
varies in time according to r1 = 3i + 3j t + 2jt2 where t is in
seconds and r is in centimeters. At the same time, the vector
position of a 5.00 g particle varies as r2 = 3i − 2it2 − 6jt. (a)
Determine the vector position of the center of mass at t = 2.40.
(b) Determine the linear momentum of the system at...
The vector position of a 3.05 g particle moving in the xy plane varies in time...
The vector position of a 3.05 g particle moving in the xy plane
varies in time according to r with arrow1 = 3i + 3j t + 2jt2 where
t is in seconds and r with arrow is in centimeters. At the same
time, the vector position of a 5.15 g particle varies as r with
arrow2 = 3i − 2it2 − 6jt.
The vector position of a 3.90 g particle moving in the xy plane varies in time...
The vector position of a 3.90 g particle moving in the xy plane
varies in time according to r with arrow1 = 3i + 3j t + 2jt2 where
t is in seconds and r with arrow is in centimeters. At the same
time, the vector position of a 5.60 g particle varies as r with
arrow2 = 3i − 2it2 − 6jt.
2). A particle moving on the x-axis has a time-dependent position (t) given by the equation...
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?
If c = 5 and b = 1. From ti = 0s to tf...
1. A particle is moving with the given data. Find the position of the particle. a(t)=2t+7,...
1. A particle is moving with the given data. Find the position
of the particle.
a(t)=2t+7, s(0)=8, v(0)=-3
2.Find f
f'(x)=1 sqrt(1-x2) , f(1/2)=8
The position of a particle moving along a line (measured in meters) is s(t) where t...
The position of a particle moving along a line (measured in
meters) is s(t) where t is measured in seconds. Answer all parts,
include units in your answers.
s(t)=2t^3 +6t^2 −48t+7 −10<t<10
(a) Find the velocity function.
(b) Find all times at which the particle is at rest.
(c) On what interval is the particle moving to the right?
(d) Is the particle slowing down or speeding up at t = −1
seconds?
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