We would like to know the velocity of the block when it reaches some position x. Finding this requires an integration. However, acceleration is defined as a derivative with respect to time, which leads to integrals with respect to time, but the force is given as a function of position. To get around this, use the chain rule to find an alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx.

Answer:

An alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex] is [tex]a_x=v_x \frac{dv_x}{dx}[/tex]

Step-by-step explanation:

We know that :

[tex]a_x=\frac{dv_x}{dt}[/tex]

Now we are supposed to find an alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex]

So, We will use chain rule over here :

[tex]a_x=\frac{dv_x}{dt}\\a_x=\frac{dv_x}{dt} \times \frac{dx}{dx}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt} [\frac{dx}{dt}=v_x]\\a_x=\frac{dv_x}{dx} \times v_x\\a_x=v_x\frac{dv_x}{dx}[/tex]

Hence an alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex] is [tex]a_x=v_x \frac{dv_x}{dx}[/tex]

The alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx is [tex]a_x = v_x \frac{dv_x}{dx}[/tex]

Here we used the chain rule:

It is the basic method for differentiating a composite function. Here the first factor on the right, Df(g(x)), represents that the derivative of f(x) is first found and then x, wherever it arises, is replaced by the function g(x).

So,

[tex]a_x = \frac{dv_x}{dt}\\\\ = \frac{dv_x}{dt} \times \frac{dx}{dx}\\\\= \frac{dv_x}{dx} \times \frac{dx}{dt}\\\\ = \frac{dv_x}{dx} \times \frac{dx}{dt} (\frac{dx}{dt} = v_x)\\\\ = \frac{dv_x}{dx} \times v_x\\\\= v_x\frac{dv_x}{dx}[/tex]

Learn more about time here: https://brainly.com/question/11325462

A box of spaghetti at the grocery store is purchased for $1.60 wholesale and is marked up by 60 percent. Then, the store marks down the item by 20 percent. A customer wants to buy three boxes of spaghetti. How much will the customer pay, including paying 8 percent sales tax? Round your answer to the nearest cent.

Look at the table below.

Steps
Moses’s work
Step 1
1 dollar and 60 cents (1.6) = 2 dollars and 56 cents
Step 2
2 dollars and 56 cents (0.80) = 2 dollars and 5 cents
Step 3
2 dollars and 5 cents (3) = 8 dollars and 20 cents
Step 4
8 dollars and 20 cents (1.08) = 8 dollars and 86 cents

In which step did Moses first make a mistake in his work?
Step 1
Step 2
Step 3
Step 4

Which number is rational, an integer, and a real number?
A. 5/7
B. There is no such number.
C. -5
D. 1.5

Find the coordinates of the midpoint of if A(–4, 7) and S(5, 3).

A party of 20 adults and 15 children celebrates at a restaurant. Each table in the restaurant seats 4 people. How many tables will the party use?

At the supermarket you can fill your own honey bear container. A customer buys 12 oz of honey for $5.40. i need help.

Find DF
Segment addition

There are two necklaces Maria wants to buy. One is $28.66 and the other is $19.39. She has a coupon for $5 off the total bill when you purchase two items. If she buys both, how much will she owe before taxes?​

The cost of renting a car is $20 to take the car and $4 for every hour that it is rented. The total amount Lucie paid was 546. For how many hours did Lucie have the car?

a. Define your variable.
b. Write an equation and solve.
c. Write a sentence to interpret your results.

I’m confused how to do ratios

Carlos cut Start Fraction 5 Over 12 End Fraction of a yard of cloth into 5 pieces of equal length. What was the length of each piece of cloth?

Start Fraction 1 Over 60 End Fraction of a yard
Start Fraction 1 Over 25 End Fraction of a yard
Start Fraction 1 Over 12 End Fraction of a yard
One-fifth of a yard

If the sum of three consecutive numbers is 852, what is the middle one?

Help me easy math problem

if side of the triangle in 8cm and side 2 is 5cm, then what is the possible range for the length of the third side of the triangle?​

Which is the correct chemical equation for photosynthesis?

48t-18=57t-81 equal what? t=-38, t=63, t=-7, t=38, t=19, or t=7

The length of a rectangle is 3.7 inches when rounded to the nearest tenth of an inch.

In a group of five students who took the same test, four of the scores were 85, 92, 81, and 95. If the average of the five students was 89, what was the score of the fifth student?

Solve by taking the square too of both sides.
3(c+3)^2-81=0

Isabella types 423 words in 9 minutes. What is Isabella's typing rate in words per minute? HELP

Help out
It is due at 7:00​

Which set of numbers best describes the possible values of x in the equation below?
[x-1] = [x]

a. all integer values of x
b. all real number values of x
c. only negative values of x
d. only non-integer values of x

whats the square root of 10?? For each to the nearest 0.05.​

Simplify the expression and enter your answer below.
(191/99

Write an
equivalent expression by distributing the "_' "sign outside the parentheses:
- (9r – 3.2s) + 4

38.5 divided by 0.5 simplified

i need help please!!

Solve –8y + 3 > –5.

A. {y | y < –1}
A. {y | y < –1}

B. {y | y > 1}
B. {y | y > 1}

C. {y | y > –1}
C. {y | y > –1}

D. {y | y < 1}

A store plans to sell two different game consoles, the YuuMi and the ZBox. The store’s wholesale cost for a YuuMi is $250, and the store can sell one for $295. The ZBox’s wholesale price is $400, and the store can sell it for $450. The store’s marketing research indicates that the total monthly demand for game consoles will not exceed 250 units sold. The store’s financial manager does not want to invest more than $70,000 in inventory costs for game consoles. How many of each game console should the store stock in order to maximize their profits, and what is their maximum monthly profit?
Constraints:

Objective formula:

PLEASEE HELP ME AS FAST AS POSSIBLE! According to the fundamental theorem of algebra, how many solutions does this polynomial have?

Btw sorry about the bad lighting

sara got 32 question out of 36. what was the percentage she got correct