Mathematics, 31.08.2019 23:30 Jessieeeeey

Aparticle moves along the x-axis so that at any time t, measured in seconds, its position is given by s(t) = 4sin(t) - cos(2t), measured in feet. what is the acceleration of the particle at time t = 0 seconds?

Answers: 1

Show answers

Answers

Answer from: tanyadeewill

The acceleration of the particle at time t = 0 seconds is:

4 feet per square second.

i.e. 4 ft/s²

Step-by-step explanation:

We are given a position function in terms of the time t as:

$s(t)=4\sin (t)-\cos (2t)$

Now, we are asked to find the acceeleration of the particle at time t = 0 seconds.

We know that the acceleration of a particle is given by:

$a=\dfrac{d}{dt}v$

where v is the velocity of the particle which is calculated by:

$v=\dfrac{d}{dt}s$

Hence, we get:

$a=\dfrac{d}{dt}(\dfrac{d}{dt}s)\\\\i.e.\\\\a=\dfrac{d^2}{dt^2}s\\\\i.e.\\\\a=s''(t)$

i.e. the acceleration of the particle is the double derivative of the position.

$s'(t)=4\cos (t)+2\sin (2t)$

and

$s''(t)=-4\sin (t)+4\cos (2t)$

i.e.

$a(t)=-4\sin (t)+4\cos (2t)\\\\i.e.\ at\ t=0\ we\ have:\\\\a(0)=-4\sin 0+4\cos 0\\\\i.e.\\\\a(0)=4$

Answer from: Quest

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

Answer from: Quest

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 $\sqrt{x}$ and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 $\sqrt{x}$ is shifted from its position in all the four options.

Another question on Mathematics

Mathematics, 21.06.2019 16:00

Given right triangle xyz, which correctly describes the locations of the sides in relation to

Answers: 1

Answer

Mathematics, 21.06.2019 17:30

Thelime contains the point(-3,0) and parallel x-3y=3( show all work)

Answers: 3

Answer

Mathematics, 21.06.2019 19:50

The probability that an adult possesses a credit card is .70. a researcher selects two adults at random. by assuming the independence, the probability that the first adult possesses a credit card and the second adult does not possess a credit card is:

Answers: 3

Answer

Mathematics, 21.06.2019 20:00

Bring the fraction a/a-4 to a denominator of 16-a^2

Answers: 1

Answer

You know the right answer?

Aparticle moves along the x-axis so that at any time t, measured in seconds, its position is given b...

Questions