Question

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)=

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) = 4t, et, e−t v(0) =
0,0,−5 r(0) = 0,1, 4

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.

A moving particle starts at an initial position
r(0) = <1, 0, 0> with initial velocity
v(0) = i - j +
k. Its acceleration is a(t) = 4t
i + 4t j +
k.
Find its velocity, v(t), and position,
r(t), at time t.

Find the position vector of a particle that has acceleration
2i+4tj+3t^2k, initial velocity v(0)=j+k and initial position
r(0)=j+k

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].

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^tk, t = 0
(b) r(t) = 〈t^5 ,sin(t)+ t ^ cos(t),cos(t)+ t^2 sin(t)〉, t =
1

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
]

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

A particle is moving along a straight line and has acceleration
given by a(t) = 20t^3+12t^2}. Its initial velocity is v( 0 ) = 4 m
/ s and its initial displacement is s( 0 ) = 5 m. Find the position
of the particle at t = 1 seconds.

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