Could the table of (x,y) pairs

The position function of a particle in rectilinear motion is given by s(t) = 2t3 – 21t2 + 60t + 3 for t ≥ 0 with t measured in s

Norma-Jean [14]

The positions when the particle reverses direction are:

$s(t_1)=55ft\\\\s(t_2)=28ft$

The acceleraton of the paticle when reverses direction is:

$a(t_1)=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=18\frac{ft}{s^{2}}$

Why?

To solve the problem, we need to remember that if we derivate the position function, we will get the velocity function, and if we derivate the velocity function, we will get the acceleration function. So, we will need to derivate two times.

Also, when the particle reverses its direction, the velocity is equal to 0.

We are given the following function:

$s(t)=2t^{3}-21t^{2}+60t+3$

So,

- Derivating to get the velocity function, we have:

$v(t)=\frac{ds}{dt}=(2t^{3}-21t^{2}+60t+3)\\\\v(t)=3*2t^{2}-2*21t+60*1+0\\\\v(t)=6t^{2}-42t+60$

Now, making the function equal to 0, to find the times when the particle reversed its direction, we have:

$v(t)=6t^{2}-42t+60\\\\0=6t^{2}-42t+60\\\\0=t^{2}-7t+10\\(t-5)*(t-2)=0\\\\t_{1}=5s\\t_{2}=2s$

We know that the particle reversed its direction two times.

- Derivating the velocity function to find the acceleration function, we have:

$a(t)=\frac{dv}{dt}=6t^{2}-42t+60\\\\a(t)=12t-42$

Now, substituting the times to calculate the accelerations, we have:

$a(t_1)=a(2s)=12*2-42=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=12*5-42=18\frac{ft}{s^{2}}$

Now, substitutitng the times to calculate the positions, we have:

$s(t_1)=2*(2)^{3}-21*(2)^{2}+60*2+3=16-84+120+3=55ft\\\\s(t_2)=2*(5)^{3}-21*(5)^{2}+60*5+3=250-525+300+3=28ft$

Have a nice day!

3 0

3 years ago

What did the Scout say after fixing the little old ladies bicycle horn

wel

the scout said beep repaired

5 0

3 years ago

A delivery truck is stocked with boxes of leather footballs. The graph shows the relationship between the number of footballs an

pashok25 [27]

Answer:

21

Step-by-step explanation:

To find the answer, you'd have to continue tracing the diagonal line until it intersects with the vertical line that corresponds to the number 3.

If you do that, you'll see that in3 boxes, there are 21 footbals.

You can also calculate it mathematically:

If you have 7 balls per box as shown in the graph, you just have to multiply 7 by 3 to know how many balls you'll find in 3 boxes. 7 * 3 = 21.

Hope it helped,

BioTeacher101

6 0

3 years ago

Read 2 more answers

Find the perimeter of a quadrilateral with vertices at C (−2, 1), D (2, 4), E (5, 0), and F (1, −3).

antoniya [11.8K]

The perimeter of the quadrilateral with vertices at C (−2, 1), D (2, 4), E (5, 0), and F (1, −3) is 20units.

Option C) is the correct answer.

<h3>What a quadrilateral?</h3>

A quadrilateral is simply a polygon with four sides, four angles, and four vertices.

To get the perimeter, we simply add the values of the four side.

Given that;

The vertices are at C (−2, 1), D (2, 4), E (5, 0), and F (1, −3).

To get the dimension between the given coordinates, we use;

d = √((x2 -x1)² +(y2 - y1)²)

For length CD, DE, EF and FC

CD = √((2 - (-2))² + (4 - 1)²) = √( 16+9) = √25 = 5

DE = √((5 - 2)² + (0 - 4)²) = √( 9+16) = √25 = 5

EF = √((1 - 5)² + (-3 - 0)²) = √( 16+9) = √25 = 5

FC = √((-2 - 1)² + ( 1 - (-3))²) = √( 9+16) = √25 = 5

Perimeter of the quadrilateral = CD + DE + EF + FC

Perimeter of the quadrilateral = 5 + 5 + 5 + 5

Perimeter of the quadrilateral = 20units

Therefore, the perimeter of the quadrilateral with vertices at C (−2, 1), D (2, 4), E (5, 0), and F (1, −3) is 20units.

Option C) is the correct answer.

Learn more about area of rectangle here: brainly.com/question/27612962

#SPJ1

6 0

2 years ago

Read 2 more answers

The isosceles trapezoids, ABCD and EFGH, are similar quadrilaterals. The scale factor between the trapezoids is 2:3, = 6 centime

Bingel [31]

Answer:

Part A) see the explanation

Part B) see the explanation

Part C) The perimeter of trapezoid ABCD is 32 centimeters and the perimeter of trapezoid EFGH is 48 centimeters

Step-by-step explanation:

<u><em>The complete question is</em></u>

The isosceles trapezoids, ABCD and EFGH, are similar quadrilaterals. The scale factor between the trapezoids is 2:3, GH = 6 centimeters, AD = 8 centimeters, and AB is three times the length of DC

Part A) Write a similarity statement for each of the four pair of corresponding sides

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

The corresponding sides are

AB and EF

BC and FG

CD and GH

AD and EH

so

$\frac{AB}{EF}=\frac{BC}{FG}=\frac{CD}{GH}=\frac{AD}{EH}$