In: Math

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. |

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) = 2 cos(t), 2t, 2 sin(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 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 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 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.

(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 = 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....

1.
Describe the Velocity vector and Acceleration vector of ball being
thrown straight up in the air and then coming back down.
2. A tennis ball is being swung around in a circle in uniform
circular motion. Describe the direction of the linear velocity
vector, the linear acceleration vector, and the centripetal
(radial) acceleration vector.
3. Which pulls harder gravitationally, the Earth on the Moon,
or the Moon on the Earth?
4. If I double the force I apply pushing...

the position of a particle when t=0 is 9.0m and its velocity is
3.0 m/s. from t=0 to t=3.5s the acceleration of a particle is a= 8
+ 6t + 3t^2 + t^3 m/s^2 . From t=3.5s until it comes to rest, its
acceleration is a= -8 m/s^2 . Determine the total travel time and
the total distance.

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