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
.
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
Matlab code please
6. Find the velocity, acceleration, and speed of a particle with
the given position function. (a) r(t) = e t cos(t)i+e t sin(t)j+
tetk t = 0 (b) r(t) = 〈t 5 ,sin(t)+ t 2 cos(t),cos(t)+ t 2 sin(t)〉,
t = 1
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.
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 velocity function of a particle moving along a line is given
by the equation v(t) = t2 - 2t -3. The particle has
initial position s(0) = 4.
a. Find the displacement function
b. Find the displacement traveled between t = 2 and t = 4
c. Find when the particle is moving forwards and when it moves
backwards
d. Find the total distance traveled between t = 2 and t = 4
e. Find the acceleration function, and...
The velocity function for a particle moving along a straight
line is given by v(t) = 2 − 0.3t for 0 ≤ t ≤ 10, where t is in
seconds and v in meters/second. The particle starts at the
origin.
(a) Find the position and acceleration functions for this
particle.
(b) After ten seconds, how far is the particle from its starting
point?
(c) What is the total distance travelled by the particle in the
interval [0, 10]?