A particle moves along a line so that its position at any time is t greater than or equal to 0 is given by s(t)=-t^2+t+2 where s is measured in meters and t is measured in seconds. A) what is the initial position of the particle? B) find the velocity of the particle at any time t. C) find the acceleration of the particle at any time t. D) find the speed of the particle at the moment when s(t)=0.

Answer:

A) The initial position of the particle is 2 meters.

B) The velocity of the particle at any time t is represented by [tex]v(t) =-2\cdot t +1[/tex].

C) The acceleration of the particle at any time t is represented by [tex]a(t) = -2[/tex].

D) The velocity of the particle at the moment when [tex]s(t) = 0\,m[/tex] is -2 meters per second.

Step-by-step explanation:

A) From statement we know that [tex]s(t) = -t^{2}+t+2[/tex], where [tex]t[/tex] is the time, measured in seconds, and [tex]s(t)[/tex] is the distance, measured in meters. The initial position of the particle is calculated by evaluating the function presented above at [tex]t=0\,s[/tex]. That is:

[tex]s(0) = -(0)^{2}+(0)+2[/tex]

[tex]s(0) = 2\,m[/tex]

The initial position of the particle is 2 meters.

B) According to the Theory on Kinematics, we see that velocity is the rate of change of position in time. In other words, we need to derive the equation once:

[tex]v(t) =-2\cdot t +1[/tex] (1)

Where [tex]v[/tex] is the velocity, measured in meters per second.

The velocity of the particle at any time t is represented by [tex]v(t) =-2\cdot t +1[/tex].

C) And the acceleration is the rate of change of velocity in time. In other words, we need to derive the equation above:

[tex]a(t) = -2[/tex] (2)

The acceleration of the particle at any time t is represented by [tex]a(t) = -2[/tex].

D) At first we solve the function position for [tex]s = 0[/tex], that is:

[tex]-t^{2}+t+2=0[/tex] (3)

[tex](t-2)\cdot (t+1)=0[/tex]

The only reasonable root of the polynomial is [tex]t = 2\,s[/tex].

And now we evaluated the velocity function at given result:

[tex]v(2) = -2\cdot (2) +2[/tex]

[tex]v(2) = -2\,\frac{m}{s}[/tex]

The velocity of the particle at the moment when [tex]s(t) = 0\,m[/tex] is -2 meters per second.

Evaluate the expression | 9 | + | - 2|

LaNaysha makes chocolate milk by mixing 5 tablespoons of cocoa powder and 2 cups of milk.

A bag contains eleven balls labeled 1 through 11. One ball will be randomly picked.
What is the probability of picking an odd number?
Write your answer as a fraction in simplest form
? ?

the members of a tennis team have a goal of raising lease $500 for new equipment. They already have $275. The team members plan to raise more money by washing cars. They would charge $5 for each car they wash.
All I need is an equation

The question is listed in the paper.

What is the equation of this line?


y=23x

y=32x

y=−32x

y=−23x

Susan wants to rent a car for a day so she can visit her sister at Queen’s. She has called two
car-rental agencies. Rent-a-Heap charges $50 for one day, plus $0.15/km. Rent-a-Car
charges $40 for one day, plus $0.20/km. At what distance will the cost of renting a car be
the same from both companies?

Help please!!
No need to explain it btw

Ashley needs to be rise words on a vocabulary list for Spanish class she has never rise 18 of the words which is 2/3 of the list how many words are on the list

Nicole’s friend runs 3/8 of a mile, but her distance is only 3/5 of Nicole’s distance. How far does Nicole run?

The number of pens sold on Monday, p, increased 45% on Tuesday. The expression p+0.45p represents the number of pens sold on Tuesday. What is another expression that can be used to find the number of pens, p, sold on Tuesday?

Problem 3.2
Jordan is mixing water and flour to make tortillas. The
number of cups of water, w, needed for f cups of flour
is described by the equation w=0.75f.
How many cups of water are needed to mix with 4 cups
of flour?
cups of water

Para resolver un parto de chocolates iguales de manera que a cada persona le corresponda la misma cantidad y no sobre nada se hizo la cuenta hizo esta cuenta 32%6= 5 indica cuantos chocolates se podrian haber rapartido entre cuantas personas y que cantidad toco cada una

Given the following diagram, find the missing measure.
2.
m_1= 30°, m 2 = 45°, m 3 =

What are the solutions to the quadratic equation 0=(x−4)(x+2)?

Select all that apply.

x=2
x=−2
x=−4
x=0
x=4

PLEASE HELP 100 POINTS AND BRAINLIEST.



NOW THAT UR HERE, THIS GUY WILL BE IN YOUR HOME TONIGHT SO LOCK THE DOORS :)...................

please help!
(picture attached)

I’ll mark brainliest! Please help !

Enter the equation of the line in slope-intercept form.

Slope is 5, and (3, 1) is on the line.

The equation of the line is y

You need 333 sticks of butter for every 242424 cookies you bake.
how many cookies would i have with 5 sticks of butter.

by selling a book for ₹100 a Man gain ₹25 his gain is​

3-(81-2)827x()2-z7221

help! need help fast

Ospreys are birds that catch and eat fish. An osprey dived from a height of 36 feet above the surface of a lake to a
depth of 4 feet below the surface. What distance did the osprey travel during that dive?
A-144 feet
B. -9 feet
C. 32 feet
D. 40 feet

what is the answer to this question?

(3-i)+(1-2i) =
O 4 - 3i
O 4 +3i
O 4+i

(b − 1)² + a^2 ; use a = 6, and b = 1

5m + 4 = 7m + 6 solve for m

What is the slope? please make sure you explajn

What is the domain of Graph 1