Suppose we are told that the position of an object (x) moving with an acceleration a is proportional to some power of a, say an and some power of t, say tm. Determine the values of n and m and write the simplest form of an equation for the position.

Answers

Answer 1

(a) The value of n is 1 and the value of m is 2

(b) The simplest form of an equation for the position is [tex]at^2[/tex]

The given expression:

[tex]x = a^nt^m[/tex]

To find:

the values of a values of n and msimplest form of the equation

The values of n and m will be calculated using the dimensions of accelerations, position and time.

The dimension of acceleration, [tex]a = LT^{-2}[/tex]The dimension of position, x = LThe dimension of time, t = T

(a) the values of n and m are calculated as follows:

[tex]x = a^n t^m\\\\ L = [LT^{-2}]^n [T]^m\\\\L = [L]^n [T^{-2n}][T]^m\\\\L = [L]^n[T^{m-2n}]\\\\L^1T^0 = [L]^n[T^{m-2n}]\\\\L^1 = L^n\\\\n = 1\\\\T^0 = T^{m-2n}\\\\0 = m - 2n\\\\0 = m- 2(1)\\\\0 = m- 2\\\\m = 2[/tex]

(b) The simplest form of an equation for the position can be written as;

[tex]x = a^n t^m\\\\x = a^1 t^2\\\\x = at^2[/tex]

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Related Questions

60.96-mile distance in kilometers

Answers

Answer:

98.105610 Kilometers

Explanation:

Rounded to 8 digits

Answer:

98.11 km

Explanation:

60.96 mi (5280ft/mi)(12 in/ft)(2.54 cm/in)(1 m/ 100cm)(1 km/1000 m) = 98.10561024 km

however, reporting this precision to the nearest hundred millionth of a kilometer is silly as we only know the mile dimension to the nearest hundredth of a mile.

A hundredth of a mile is 5280/100 = 52.8 ft or just over 16 m

It would only be a little bit of a presumption to give our precision to the nearest 10 meters as I have done.

This also fits neatly into the significant digits rule. Both the original dimension and the converted dimension have four significant digits.

9.1 x 105 – 7.2 x 105
=

Answers

Answer:

1.9 x 10⁵

Explanation:

I ASSUME your question is supposed to read

9.1 x 10⁵ – 7.2 x 10⁵ =

9.1 - 7.2 = 1.9 and the powers are the same so just tag them along

its the same as

910000 - 720000 = 190000

1.9 x 105 could be another possibility if the question is actually posed correctly.

What is the amount of force exerted by gas particles?

Answers

Answer:

Pressure is the force divided by the area on which the force is exerted, and temperature is measured with a thermometer. We gain a better understanding of pressure and temperature from the kinetic theory of gases, which assumes that atoms and molecules are in continuous random motion.

Name another way that energy is made

Answers

Answer:

The three major categories of energy for electricity generation are fossil fuels (coal, natural gas, and petroleum), nuclear energy, and renewable energy sources. Most electricity is generated with steam turbines using fossil fuels, nuclear, biomass, geothermal, and solar thermal energy.

Explanation:

Solar

Wind

Geothermal

Hydrogen

TidaWave

Hydroelectric

Biomass

A positively charged glass rod is bought close to a suspended metal needle. What
can we say about the charge on the needle given that the needle is
a) attracted ?
b) repelled ?

Answers

Answer:

attracted

Explanation:

opposite charges attract each other when the rub against each other

Answer:

This depends because the electrostatic force obeys the principle that states that force between both of the particles does not get affected by the charges of the other thus if the needle is getting attracted it possess negative charges( the opposite charge) .And if they repel it means they have the same charges ( positive charges).

A light bulb uses 40.0 W of power when connected to a 110 V (DC) outlet. If the same bulb is connected to a European 220 V outlet, how much power will the bulb use?​

Answers

If the bulb's resistance doesn't change, the power it uses is proportional to the square of the voltage. So doubling the voltage quadruples the power.

On 220 V, the bulb uses (4 • 40w)= 160 W.

It glows very brightly.

For a very short time.

Because it also gets very hot, and burns out.

After a few seconds, it uses zero watts.

Answer:

160

Explanation:

Acellus

câu 1 vẽ sơ đồ trình bày nguyên lý làm việc các thông số và đặc điểm của mạch chỉnh lưu cầu 1 pha
câu 2 vẽ sơ đồ trình bày nguyên lý làm việc của bộ nghịch lưu áp 1 pha

Answers

Answer:gang gang father gang

Explanation:idek cuh

What is the velocity of a car that traveled a total of 75 kilometers north in 1.5 hours?

What are you solving for?
What’s the equation?
Show work!
Help pleaseee!

Answers

Answer:

50km/hr is the velocity of a car that traveled a total of 75 km North in 1.5 hours.

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