Question

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.

Answer #1

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].

If u(t) = sin(6t), cos(2t), t and v(t) = t, cos(2t), sin(6t) ,
use Formula 4 of this theorem to find d dt u(t) · v(t) .

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

A particle that moves along a straight line has velocity v ( t )
= t^2e^− 2t meters per second after t seconds. How many meters will
it travel during the first t seconds (from time=0 to time=t)?

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)

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

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.

A particle is moving according to the given data a(t) = sin t +
3 cos t, x(0) = 0, v(0) = 2.
where a(t) represents the acceleration of the particle at time
t. Find v(t), the velocity of the particle at time t, and x(t), the
position of the particle at time t.

The position (in meters) of an object moving in a straight
line
s(t)=√ 3t+1 −2t^2+1
where t is measured in seconds.
(a) Find the average velocity on [0,1].
(b) Find the instantaneous velocity at t=1.
(c) Find the acceleration at t=1.

let r(t)=<cos(2t),sin(2t),3>
describe the shape of the path of motion of the object.
how far has the object travelled between time T= 0 and time T =
2pi?

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