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

An electromagnetic wave from space is detected with a frequency of 4.4 x 109 Hz. What is the wavelength of this wave?

Answers

Explanation:

[tex]\lambda = \dfrac{c}{\nu} = \dfrac{3×10^8\:\text{m/s}}{4.4×10^9\:\text{Hz}} = 0.068\:\text{m}[/tex]

Help meh in this question​

Answers

Radius=r=R_o/2angular velocity=w=v_omass=m

We know

[tex]\boxed{\sf K.E=\dfrac{1}{2}mv^2}[/tex]

For Rotational motion

[tex]\boxed{\sf v=r\omega}[/tex].

Putting value

[tex]\\ \qquad\quad\sf{:}\dashrightarrow K.E=\dfrac{1}{2}m(r\omega)^2[/tex]

[tex]\\ \qquad\quad\sf{:}\dashrightarrow K.E=\dfrac{1}{2}mr^2\omega^2[/tex]

[tex]\\ \qquad\quad\sf{:}\dashrightarrow K.E=\dfrac{1}{2}m\left(\dfrac{R_o}{2}\right)^2v_o^2[/tex]

[tex]\\ \qquad\quad\sf{:}\dashrightarrow K.E=\dfrac{1}{4}mv_o^2[/tex]

plzzzzzzzzzzzz somebody help, plzzzzzzzz this is important. where are the geniuses out there please help. Thanks in advance .
Four forces act as shown in the
diagram below, calculate their
resultant.
12N
10N
40
30
60°
15N
9N​

Answers

iAnswer:

The resultant vector force = 6.96i - 9.27j

The magnitude = 11.6N

The direction= -53.1 °

Explanation:

i= 10×cos(30) + 15×cos(-60) + 9×cos(-90) + 12×cos(140) = 6.96

j= 10×sin(30) + 15×sin(-60) + 9×sin(-90) + 12×sin(140) = -9.27

Bradd stands 6km west of a flagpole, and runs towards it with a speed of 9km/h. Pitt stands 5km east of the flagpole, and runs towards it with a speed of 8km/h. At what displacement from the flagpole are they when they meet?

Answers

Answer:

176 m west of the flagpole.

Explanation:

In exact and precise interpretation of the question the answer is 0 m as they would both crash into the pole when they got there and presumably stop having suffered broken noses and serious groin injuries.

However my GUESS as to the intent of the question is that the first to reach it will sidestep the flagpole slightly and continue on their current path until they meet and slap a high five as they pass one another.

In that case, they have 6 + 5 = 11 km to traverse at a closing rate of 9 + 8 = 17 km/hr.

They will meet in 11 km / 17 km/hr = 0.647 hrs

Bradd will have covered 9 km/hr(0.647 hr) = 5.823 km

meaning that they will be 6 - 5.823 = 0.176 km or 176 m west of the flagpole.

Pitt will have covered 8 km/hr(0.647 hr) = 5.176 km

meaning they will be 5 - 5.176 = - 0.176 km east which equals 0.176 km west of the flagpole


Select the best answer for the question.
17. How many mL of HEPARIN 10,000 units/mL are needed for a 7,000 unit dose?
O A.0.7
O B. 0.07
O C.7
O D. 0.007

Answers

The answer is 7 because if it has zero at the beginning then its a lower number

0.7 mL of HEPARIN 10,000 units/mL is needed for a 7,000 unit dose.

To calculate the volume of HEPARIN 10,000 units/mL needed for a 7,000 unit dose, we can use the formula:

Volume (mL) = Dose (units) / Concentration (units/mL)

Given that the dose is 7,000 units and the concentration of HEPARIN is 10,000 units/mL, we can plug these values into the formula:

Volume (mL) = 7,000 units / 10,000 units/mL

Volume (mL) = 0.7 mL

So, 0.7 mL of HEPARIN 10,000 units/mL is needed for a 7,000 unit dose. However, none of the provided answer choices match exactly with 0.7 mL. The closest option is B. 0.07 mL, which is one-tenth of 0.7 mL. Therefore, the correct answer is B. 0.07 mL.

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For an electron, magnitude of force on it
is
Select one
• Bev
bev
Be
BIL

Answers

Answer:

F = Bev

Explanation:

B is magnetic field density

e is the electron charge

v is the electron velocity

An acetate rods rubs against a cloth. What type of charge will the rod end up with?
A. Positive
B. Negative
C. Not enough info
D. Neutral

Answers

Answer:

I believe it's A

Explanation:

........

Explain why selling cereal by mass rather then by volume be more fair to customers

Answers

Answer:

Simple, there could be air in the package and volume would record that, whereas mass would count the mass of the cereal and discount the air.

principle of electroplating​

Answers

dnxjjc cjgnjgjnffjnfkfmgkcknsmksjs dmxmcmfkcnfjcnfjfnfjf in jfnfifnfifnf

Answer:

Electroplating is the method of depositing one metal over another in the presence of a metal salt (in aqueous solution). The water molecule is released as the final product in this process. As a consequence, electroplating is based on the theory of hydrolysis.

A spring with spring constant 120 N/m and unstretched length 0.4 m has one end anchored to a wall and a force F is applied to the other end.

Required:
a. If the force F does 250 J of work in stretching out the spring, what is its final length?
b. If the force F does 250 J of work in stretching out the spring, what is the magnitude of F at maximum elongation?

Answers

(a) The work done by F in stretching the spring a distance x is

W = 1/2 (120 N/m) x ²

so F performs 250 J of work on the spring, then

250 J = 1/2 (120 N/m) x ²   ==>   x ² ≈ 4.17 m²   ==>   x2.04 m

(b) In order for F to perform 250 J of work, its magnitude must be

F = (120 N/m) (2.04 m) ≈ 245 N

what is suvat in physics ?​

Answers

"SUVAT" is an acronym from the variables:

S = displacement,
U = initial velocity,
V = final velocity,
A = acceleration,
T = time.

Pls give me a brainliest if this helped thx

The type of force that will not cause a change in the speed of an object.

Answers

Explanation:

Balanced forces will cause no change in the speed of an object.

Who has greater displacement, an astronaut who has just completed an orbit of the earth or you when you have just traveled from home to school?

Answers

Answer:

Explanation:

This is going to sound like an absurd answer, but sometimes physics can be a little strange.

This answer is weird because of the definition of displacement. It means the distance from the starting point to the ending point, disregarding what happened in between. The point is that the astronaut is at the starting point of his orbit. By definition the starting and ending points are the same. His displacement is 0.

So the answer is you have the greater displacement when you walked one way to school.  The starting point and the ending point are different. You have gone further.

However just to make things a little nasty, when you walk home again, your displacement will be the same as the astronaut's -- 0 meters because you will be right back where you started from.

You that just traveled from home to school has greater displacement than the astronaut.

Displacement is defined as the change in the position of an object.

An astronaut who completed an orbit of the earth, has moved from an initial position x₁ and returned to the same position x₁ because Earth is assumed to be spherical. To complete an orbit of the Earth, the astronaut must return to his initial position since he will move round the Earth.

The displacement of the astronaut is zero because x₁ - x₁ = 0

For you that have just traveled from home to school, BUT haven't returned, your displacement is greater,.

Let's say the distance from your home to school = y

Your initial position at your home = 0

your displacement = y - 0 = y

Thus, you that just traveled from home to school has greater displacement than the astronaut.

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The average speed, correspondence to the average speed in a trajectory. True or false?

Answers

Answer:

hablo españolete telo ease

Explanation:

Which of the following is an example of a physical change?


Burning charcoal.

Dissolving sugar in water.

Cooking a hamburger.

Car Rusting.

Answers

Answer:

Dissolving sugar in water is an example of a physical change .

.......

A human hair is approximately 50 pm in diameter. Express this diameter in meters.

Answers

A human hair is approximately 50 μm = 5 × 10⁻⁵ m  in diameter

Driving home from school one day, you spot a ball rolling out into the street . (See the figure below) You brake for 1.50 s , slowing your 950-kg car from 16.0 m/s to 9.50 m/s.

a)What was the magnitude of the average force exerted on your car during braking?

b)What was the direction of the average force exerted on your car during braking?

c)How far did you travel while braking?

Answers

Answer:

a) 4116.67 N

b) negative (assuming car is traveling in positive direction)

c) 19.125 m

Explanation:

Part A)

We can find the average force exerted on the car by using Newton's 2nd Law: F = ma.

We have the mass (950 kg) but we do not have the acceleration. Let's solve for this using kinematics.

We have the time during braking, the initial and final velocity, and we need to find the acceleration. To do this, we can use the following equation: v = v₀ + at.

v (final velocity) = 9.50 m/sv₀ (initial velocity) = 16.0 m/st (time) = 1.50 s a = ?

Substitute these values into the equation.

v = v₀ + at9.50 m/s = 16.0 m/s + a (1.50 s) 9.50 = 16.0 + 1.50a -6.50 = 1.50a a = -4.333333... m/s²

The car's acceleration during the braking period is -4.33 m/s², assuming the car is traveling in the positive direction.

Now, we can use this to plug into Newton's 2nd Law to find the force exerted on the car.

F = maF = (950 kg) (-4.33...) F = -4116.666667 N

The magnitude of the average force exerted on the car while braking is the absolute value, so it is 4116.67 N.

Part B)

The direction of the average force is denoted in the negative sign. It is opposite the direction of the car's motion. Assuming that the car is traveling in the positive direction, the direction of the average force exerted on the car is in the negative direction since this force is slowing the car down while braking.

Part C)

We can find the distance traveled during the braking period by using another kinematic equation.

We have the initial and final velocity, and the time traveled, so we can use this equation: Δx = v_avg · t.

Note that v_avg is the same thing as (v + v₀) / 2.

Substitute the known values into the equation.

Δx = [(9.50 + 16.0)/2] · 1.50 Δx = 12.75 · 1.50Δx = 19.125 m

The car traveled 19.125 m while braking.

If a body travels 18 km in 1 hrs, find the average velocity of the body in m/s

Answers

Answer:

Explanation:

18 km/hr (1000 m/km)(1 hr/3600 s) = 5 m/s

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.

If the toy car weighs 250g and has a kinetic energy of 2.0 J, what is its velocity

Answers

Explanation:

Kinetic energy (J) = 2j

mass= 250g

velocity=?

1kg=1000g

mass= 250/1000

mass=0.25kg

Kinetic energy (J) = ½ x mass (kg) x [velocity]² (m/s)

2=1/2 × 0.25× [velocity]²

2=0.125× [velocity]²

[velocity]² = 2/0.125

[velocity]²=16

velocity= (16)^1/2

velocity= 4 m/s

A child throws a tennis ball straight down with a speed of 14.8 m/s. It takes 1.5 seconds to reach the ground. What is its velocity when it reaches the ground?

Answers

Answer:

-14.8 m/s

Explanation:

Unless this is a trick question the initial velocity is 14.8 m/s.  Velocity is a vector quantity, i.e. it has a magnitude AND direction.  Speed which is a scalar is certainly 14.8 m/s.  The direction of the vector depends on the axis of co-ordinates chosen; consequently velocity might be said to be - 14.8 m/s

Carnot Engine: A Carnot cycle consists of 179) A) four adiabats. B) two adiabats and two isobars. C) four isotherms. D) two adiabats and two isotherms. E) two isobars and two isotherms

Answers

Answer:

which question is this

Explanation:

I don't understand sorry

Pls help lsplsplsplsplsplsplsplps

Answers

hey there! the correct answer would be ozone! hope this helps!!

write any three differences between metals and nonmetals​

Answers

Metals Non-metals

They are solid at room temperature. They may be solid, liquid and gas at room temperature.

They have high melting and boiling points. They have low melting and boiling points.

They are good conductors of heat and electricity. They are bad conductors of heat and electricity.

What is the velocity of an object that moves from 73 m to 62 m in 15 s?

Answers

Answer:

Below

Explanation:

You can use this formula to find the velocity of an object

     velocity = displacement / change in time

For this problem, we need to find displacement first

To find displacement all you need to do is find the difference between the two distances!

So our displacement here would be

     73 - 62 = 11 m

Now that we have displacement we can find velocity

      velocity = 11 / 15

                    = 0.733333....

                    = 0.73 m/s

Hope this helps! Best of luck <3

The velocity of an object that moves from 73 m to 62 m in 15 s is 0.73 m / s.

What is velocity?

When an item is moving, its velocity indicates how quickly its location is changing as seen from a specific point of view and as measured by a specific unit of time.

If a point travels a specific distance along its path in a predetermined amount of time, its average speed throughout that time is equal to the traveled distance divided by the travel time. For instance, a train traveling 100 km in two hours is moving at an average speed of 50 km/h.

Given:

The distance of the object = 73 m to 62 m,

The time taken by the object, t = 15 s,

Calculate the displacement of the object = 73 - 62 = 11 m

Calculate the velocity by the formula given below,

[tex]v = d /t[/tex]

v = 11 / 15

v = 0.73 m / s

Therefore, the velocity of an object that moves from 73 m to 62 m in 15 s is 0.73 m / s.

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is lightning man-made or Natural occuring?
claim:
give scientific reason:
evidence:​

Answers

Answer:

give me brainliest

Explanation:

Lightning is a naturally occurring electrostatic discharge during which two electrically charged regions, both in the atmosphere or with one on the ground, temporarily equalize themselves, causing the instantaneous release of as much as one gigajoule of energy. ... Humans have deified lightning for millennia.  

Lightning happens when the negative charges (electrons) in the bottom of the cloud are attracted to the positive charges (protons) in the ground.

A small piece of aluminum (atomic number 13) contains 10^15 atoms (The atomic number is the number of protons; it determines the (positive) electric charge of the nucleus and, thus, the number of electrons in a neutral atom.) If the piece of aluminum has a net positive charge of 3.0 uc what fraction of the electrons that the aluminum had when it was neutral would have had to be lost?

Answers

Answer:

3 micro coulombs = 3 * 10E-6 coulombs     charge of aluminum

13 * 10E15 * 1.6 * 10E-19 = 2.08 E-3 Coulombs - charge of atoms in Al

3 * 10E-6 / 2.08 * E-3 = 1.44 * E-3 = .00144 = .144 %

.00144 of the original electrons would have to be lost

An 8-ohm resistor is connected to a 120-volt circuit. What current will it draw?

Answers

Answer:

15 A (15 amperes of current)

Explanation:

From Ohm's Law,

Voltage, V = Current, I × Resistance, R

Making Current, I the subject:

Current, I = Votage, V/ Resistance,R

= V/R

= 120volts /8ohms

= 15 A

b. What is measurement? Why measurement is important in our daily life? 3 Write the sunits of electric current and​

Answers

Explanation:

Please mark me as brainlyest

Answer:

- Measurement is a comparison of an unknown quantity with a known fixed quantity of the same kind. The value obtained on measuring a quantity is called its magnitude. Magnitude of a quantity is expressed as numbers in its units.

- Measurements play an important role in daily life because they are useful to do basic tasks, such as take a child's temperature with a thermometer, make time estimations, measure out medicine and find weights, areas and volumes of different materials or substances.

- Electrical Parameter Measuring Unit Unit/Symbol

Voltage                               Volt                    V or E

Resistance                       Ohm                    R or Ω

Current                               Ampere             I or i

Capacitance                       Farad              C

Explanation:

I'm not sure but hope it helps.

astone is thrown upwards with an initial velocity of 25m/s at ange of 30 to the ground. work out the stones horizantal range?

Answers

Explanation:

[tex]R = \dfrac{v_0^2}{g}\sin{2\theta} = \dfrac{(25\:\text{m/s})^2}{9.8\:\text{m/s}^2}\sin{60°}[/tex]

[tex]\:\:\:\:=55.2\:\text{m}[/tex]

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