Question

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].

Answer #1

a(t) = 2e^ −t + 4 cos(2t) − sin(2t).
Find the initial acceleration at t = 0. If time is measured in
seconds and distance is measured in meters, what units is your
answer in?
Find the velocity v(t) of the object given an initial velocity
of 2 meters per second.
Find the position s(t) of the object given an initial position
of 0 meters.

) The velocity function v(t) = −2t + 6, on the interval [1,5] is
given for a particle moving along a line. Find the distance
traveled

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) = 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

The velocity function (in meters per second) is given for a
particle moving along a line.
v(t) =
t2 − 2t −
8, 1 ≤ t ≤ 5
(a) Find the displacement. (m)
(b) Find the distance traveled by the particle during the given
time interval. (m)

The acceleration of an object (in m/s2) is
given by the function a(t)=6sin(t). The initial velocity of the
object is v(0)= −1 m/s. Round your answers to four decimal
places.
a) Find an equation v(t) for the object velocity.
v(t)= -6cos(t)+5
b) Find the object's displacement (in meters) from time 0 to
time 3.
15-6sin(3) Meters
c) Find the total distance traveled by the object from time 0 to
time 3.
? Meters
Need Help fast, please

Given that the acceleration vector is
a(t)=〈−1cos(t),−1sin(t),−2t〉
the initial velocity is v(0)=<1,0,1>
and the initial position vector is r(0)=<1,1,1>
compute:
a. The velocity vector
b. The position vector

A
particle moves in a straight line with velocity 8-2t ft/s. Find the
total displacement and total distance traveled over the time
interval [0, 7].

A particle is moving with the given data. Find the position of
the particle. a(t) = 2t + 5, s(0) = 3, v(0) = −5
s(t) =

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