Question

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**+ te^t**k**, t = 0

(b) r(t) = 〈t^5 ,sin(t)+ t ^ cos(t),cos(t)+ t^2 sin(t)〉, t = 1

Answer #1

Find the velocity and position vectors of a particle that has
the given acceleration and the given initial velocity and
position.
a(t) = 2 i +
6t j + 12t2
k, v(0) = i,
r(0) = 3 j − 6
k

Find the velocity and position vectors of a particle that has
the given acceleration and the given initial velocity and position.
a(t) = (6t + et) i + 12t2 j, v(0) = 3i, r(0) = 7 i − 3 j
v(t)=
r(t)=

Find the velocity and position vectors of a particle that has
the given acceleration and the given initial velocity and
position.
a(t) = 4t, et, e−t v(0) =
0,0,−5 r(0) = 0,1, 4

The position of a particle for t > 0 is given by →r (t) =
(3.0t 2 i ^ − 7.0t 3 j ^ − 5.0t −2 k ^ ) m. (a) What is the
velocity as a function of time? (b) What is the acceleration as a
function of time? (c) What is the particle’s velocity at t = 2.0 s?
(d) What is its speed at t = 1.0 s and t = 3.0 s? (e) What is...

6.
a) Use the given acceleration function and initial conditions to
find the position at time t = 1.
a(t) = 6i + 10j + 8k, v(0) = 4k, r(0) = 0
b) Find the arc length for r(t) = 3 cos t i + 3 sin t j, [ 0 , 6
]

If the acceleration of a particle is given by a(t)=2t-1 and the
velocity and position at time t=0 are v(0)=0 and S(0)=2.
1. Find a formula for the velocity v(t) at time t.
2. Find a formula for the position S(t) at time t.
3. Find the total distance traveled by the particle on the
interval [0,3].

please ASAP!!
Suppose that a particle has the following acceleration vector
and initial velocity and position vectors.
a(t) = 5 i +
9t k,
v(0) = 3 i
−
j, r(0)
= j + 6 k
(a)
Find the velocity of the particle at time t.
(b)
Find the position of the particle at time t.

1. (1’) The position function of a particle is given by s(t) =
3t2 − t3, t ≥ 0.
(a) When does the particle reach a velocity of 0 m/s? Explain the
significance of this value of t.
(b) When does the particle have acceleration 0 m/s2?
2. (1’) Evaluate the limit, if it exists.
lim |x|/x→0 x
3. (1’) Use implicit differentiation to find an equation of the
tangent line to the curve sin(x) + cos(y) = 1
at...

Given that the acceleration vector is a ( t ) = (−9 cos( 3t ) )
i + ( −9 sin( 3t ) ) j + ( −5 t ) k, the initial velocity is v ( 0
) = i + k, and the initial position vector is r ( 0 ) = i +j + k,
compute: the velocity vector and position vector.

Let a > b. Suppose a particle moves in an elliptical path
given by r(t) = (a cos ωt) i+(b sin ωt) j where ω > 0. Sketch
its velocity and acceleration vectors at one of the vertices of the
ellipse (±a, 0).

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