Question
In: Math
Suppose that a particle has the following acceleration vector and initial velocity and position vectors. a(t) ...
| Suppose that a particle has the following acceleration vector
and initial velocity and position vectors. a(t) = 7 i + 9t k, v(0) = 4 i − j, r(0) = j + 5 k |
| (a) | Find the velocity of the particle at time t. |
| (b) | Find the position of the particle at time
t. |
Solutions
milcah answered 3 years agoRelated Solutions
1) Find the velocity and position vectors of a particle that has the given acceleration and...
1) Find the velocity and position vectors of a particle that has
the given acceleration and the given initial velocity and
position.
a(t) = 7i+
4j, v(0) =
k, r(0) =
i
2) Find the tangential and normal components of the acceleration
vector.
r(t) = 5(3t −
t3) i +
15t2 j
Find the velocity, acceleration, and speed of a particle with the given position function. r(t) =...
Find the velocity, acceleration, and speed of a particle with
the given position function. r(t) = 2 cos(t), 2t, 2 sin(t)
Find the velocity, acceleration, and speed of a particle with the given position function. r(t) =...
Find the velocity, acceleration, and speed of a particle with
the given position function.
r(t) =
9 cos(t), 8 sin(t)
v(t)
=
a(t)
=
|v(t)|
=
Sketch the path of the particle and draw the velocity and
acceleration vectors for
t =
π
3
.
write a matlab code to find the following: initial position, initial velocity, and acceleration using the...
write a matlab code to find the following: initial position,
initial velocity, and acceleration using the algorithm and
information below
time(seconds). height(m) velocity(m/s)
0. 0.2. 2.95
algorithm:
1. Enter data in to arrays.
2. Fit the height data to a 2nd order polynomial.
3. Evaluate the polynomial at enough points to get a smooth
curve.
4. Find the velocity model by taking derivative of the height
polynomial.
5. Evaluate the velocity polynomial at enough times to get a
smooth curve
A particle moves with acceleration function a(t) = 2x+3. Its initial velocity is v(0) = 2...
A particle moves with acceleration function a(t) = 2x+3. Its
initial velocity is v(0) = 2 m/s and its initial displacement is
s(0) = 5 m. Find its position after t seconds.
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.
Create an equation for the velocity of a particle at any time t, stating the initial...
Create an equation for the velocity of a particle at any time t,
stating the initial position, which cannot equal 0. The equation
must include all of:
• Rational function
• Trigonometric function
a. Determine, using appropriate sums of rectangles, an over and
under estimation of the displacement of the particle in the first
10 seconds. i. Explain how this estimation could be made more
exact.
b. Determine the exact displacement of the particle for the
first 10 seconds, and...
(1 point) For the given position vectors r(t)r(t) compute the unit tangent vector T(t)T(t) for the...
(1 point) For the given position vectors r(t)r(t) compute the
unit tangent vector T(t)T(t) for the given value of tt .
A) Let r(t)=〈cos5t,sin5t〉
Then T(π4)〈
B) Let r(t)=〈t^2,t^3〉
Then T(4)=〈
C) Let r(t)=e^(5t)i+e^(−4t)j+tk
Then T(−5)=
Answer the following questions for an orbit with the following Position and Velocity vectors: (R =...
Answer the following questions for an orbit with the following
Position and Velocity vectors:
(R = 7626I + 4972J + 806K km, V = 0.626I - 0.690J - 6.160K
km/s)
1. Determine the size of the size (semimajor axis) of this
orbit.
2. Determine the shape (eccentricity) of this orbit.
3. Determine the inclination of this orbit.
4. Determine the right ascension of the ascending node for this
orbit.
5. Determine the argument of the perigee for this orbit.
6....
A particle moves in the xy plane with constant acceleration. At t = 0 the particle...
A particle moves in the xy plane with constant acceleration. At
t = 0 the particle is at vector r1 = (3.6 m)i + (2.8 m)j, with
velocity vector v1. At t = 3 s, the particle has moved to vector r2
= (11 m)i − (1.8 m)j and its velocity has changed to vector v2 =
(4.6 m/s)i − (6.7 m/s)j. (a) Find vector v1. vector v1 = m/s
(b) What is the acceleration of the particle? vector a...
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