6-7 Collisions and Explosions (1-D)
1. A flatcar with mass M, traveling at speed v, collides with and couples to a parked
boxcar. They move off together with a speed of 1/3 v. What is the mass of the boxcar?

When a softball is thrown from an 80-meter-high building at a velocity of 10 meters per second, the height after t seconds is 148 feet.

Velocity is a vector representation of an object's or particle's displacement with respect to time. The meter per second (m/s) is the standard unit of velocity magnitude (also known as speed). Alternatively, velocity magnitude can be expressed in centimeters per second (cm/s). The direction of movement of the body or item is defined by velocity. Speed is fundamentally a scalar number. Velocity is, in essence, a vector quantity. It is the pace at which distance changes. It is the displacement rate of change. Speed is the pace at which an item moves along a route in time, whereas velocity is the rate and direction of movement. In other words, velocity is a vector, whereas speed is a scalar number.

Here,

The maximum height the ball will reach is the vertex of the parabola s(t)=48+80t-16t2. first, we need to solve for t. The vertex of any parabola of the form f(x)=ax2+bx+c is found by using x=-b/2a. In this case, x=t, b=80 and a=-16. Substituting we get:

]t=-80/((2)(-16)--->t=-80/-32--->t=5/2

Putting this value of t in the original formula will give us the maximum height:

s(t)=48+80t-16t2

s(5/2)=48+80(5/2)-16(5/2)2

s(5/2)=48+200-16(25/4)

s(5/2)=248-100

smax=148 feet

It's height, in meters, after t seconds is 148 feet when softball is thrown off of a building that is 80 meters high at a velocity of 10 meters per second.

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The propositions P and Q are both true. P states that you can paddle one canoe down the river, and Q states that you can paddle one kayak down the river. Both of these activities are possible, making both statements true.

A proposition is a statement or assertion that expresses a judgment or opinion about a particular topic or issue. It is a type of argument used in logic and critical thinking, and is typically expressed in a declarative sentence. Propositions can be either true or false and can be used to support or reject a claim. In philosophy, propositions can also be used to explain and justify a particular belief or set of beliefs. Propositions are often used in academic and scientific discourse to communicate ideas and arguments in a concise and logical manner.

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You will likely best minimize your risk by making a two-point turn.

The greatest strategy to reduce your danger when changing lanes on a two-way street is to do a two-point turn by retreating into a driveway on your right before moving forward into the roadway.

Turnabouts are turning maneuvers in which a driver reverses the direction of a moving vehicle by making a series of motions. A turnabout accomplished by first backing into a driveway or an alley is known as a two-point turnabout. A turnabout can also be accomplished by backing into a roadway after entering an alley or driveway, albeit this method is riskier.

Turning your car around to travel in the opposite direction is known as a turnabout. When deciding to use a turnabout, take the appropriate precautions.

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C. 27 N force must be applied to lift the object.

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The solution with the lowest total ion concentration, assuming full dissociation, is 2 M aluminum sulphate.

Concentration in chemistry is defined as the abundance of an ingredient divided by the total volume of a combination. There are four sorts of mathematical descriptions: mass concentration, molar concentration, number concentration, and volume concentration. The amount of a material, such as salt, that is present in a certain amount of tissue or liquid, such as blood. When there is less water present, a material becomes more concentrated. When a person does not drink enough water, the salt in his or her urine may become more concentrated. A substance's concentration is the amount of solute contained in a given amount of solution. Molarity is the number of moles of solute in one liter of solution and is used to express concentrations.

Here,

The solution with the lowest total ion concentration, assuming full dissociation, is 2 M aluminum sulfate.

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A negative acceleration indicates that you will reduce the velocity's present value, while a positive acceleration indicates that you will increase it.

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If one could drive a Jetson's flying car at a constant speed of 160km/hr (100 mi/hr), the time it will take to drive around the Earth's equator is 250.47hours.

The time it will take to cover a certain distance can be calculated using the following formula;

Speed = distance ÷ time

According to this question, one could drive a Jetson's flying car at a constant speed of 160km/hr (100 mi/hr) across oceans and space. The distance around Earth at the Equator, its circumference, is 40,075 kilometers (24,901 miles).

Time = Distance ÷ speed

Time = 40,075km ÷ 160km/hr

Time = 250.47hours

Therefore, 250.47hours is the time it will take to cover around the Earth's equator.

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So the heat dacy can be calculated using the  winger way formula

In one day ,[tex]P_{d}(t)=\\[/tex][tex]6.65\times 10^{-3}[/tex] GW(t), In one month =[tex]P_{d}(t)=\\[/tex][tex]1.946\times 10^{-3}[/tex] GW(t) , in one year  ,  [tex]P_{d}(t)=\\[/tex][tex]2.29\times 10^{-4}[/tex] GW(t)

According to thermodynamics, heat is a type of energy that crosses a thermodynamic systems' boundary due to a temperature differential across the barrier Heat is absent in thermodynamic systems. However, the expression is also regularly used to describe the thermal energy that constitutes a system's internal energy and is reflected in the system's temperature. In all senses of the word, energy is a form of heat.

For the  decay we have winger way formula as ,

[tex]P_{d} =0.0622P_{0}[t-0.2-(t_{0}-0.2(t_{0}+t)-0.2][/tex]

[tex]P_{0}=1.5GW(t)[/tex],[tex]t_{0}=31,536,000[/tex]

[tex]P_{d}(t)=\\[/tex]thermal power generation due to beta and gamma rays

[tex]t_{0}=[/tex]time in seconds , of thermal power level before shut down

t= rime , in seconds elapsed since the shutdown

a)  In one day ,

Number of seconds ,t=86400s

so , P

[tex]P_{d}(t)=\\[/tex]0.0622 x 1.5 x [86,400-0.2-(31,536,000+86,400)-0.2]

[tex]P_{d}(t)=\\[/tex][tex]6.65\times 10^{-3}[/tex] GW(t)

b ) In one month

Number of seconds ,t=2629800s

[tex]P_{d}(t)=\\[/tex]0.0622 x 1.5 x [2629800-0.2-(31,536,000+2629800)-0.2]

[tex]P_{d}(t)=\\[/tex][tex]1.946\times 10^{-3}[/tex] GW(t)

c) In one year  

Number of seconds ,t=2629800s

[tex]P_{d}(t)=\\[/tex]0.0622 x 1.5 x [31,536,000-0.2-(15,768,000+31,536,000)-0.2]

[tex]P_{d}(t)=\\[/tex][tex]2.29\times 10^{-4}[/tex] GW(t)

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Answer: The angle at which the plane is flying relative to the tree is 19.47 degrees.

Explanation:

To calculate the angle at which the plane is flying relative to the tree, we can use the principle of trigonometry and the Pythagorean theorem. Since we know the distance from the plane to the nearest tree (60 meters), the height of the plane (10 meters), and the height of the tree (20 meters), we can use these measurements to form a right triangle with the plane, the tree, and the ground.

Using the Pythagorean theorem, we can calculate the length of the hypotenuse of the right triangle. The length of the hypotenuse is the distance between the plane and the top of the tree. The hypotenuse is calculated by the square root of (distance^2 + height of the plane^2 + height of the tree^2)

The angle we are trying to calculate is opposite to the height of the tree, therefore we can use the tangent function:

tan(angle) = opposite/adjacent

opposite = height of the tree = 20m

adjacent = distance = 60m

angle = arctan(20/60) = arctan(1/3) = 19.47122063449069 degrees

The angle at which the plane is flying relative to the tree is 19.47 degrees.

The magnitude of the charge on each bead is 7.08nc.

Given the following information:

Original length = 4.0 cm converted to m = 0.04 m

1.4 grams to kilograms = 0.0014

5.1 cm to m = 0.051 is the new length.

4.6 cm to m = 0.046 m is the final length.

e =  0.051 - 0.046

= 0.005m in length

Scientific evidence:

Gravitational acceleration = 9.8m/s²

Coulomb's constant is equal to 8.99 x 10⁹ Nm²/C²

We would use Coulomb's law to calculate the magnitude of the charge (in nC) on each bead:

First, we would calculate the spring constant of this lightweight spring

using the following formula:

W = mg = Ke

K = mg/e

K = 0.014 x 9.8 / 0.05

K = 2.744N/m

K, the spring constant, is 2.744N/m.

In terms of electrostatic force:

F = ke

F = 2.77 x 0.05

F = 0.1385

F equals 0.1385 Newton.

Coulomb's electrostatic force law.

The charge in an electric field can be calculated mathematically using the following formula:

q = √F/k x r

We get by substituting the given parameters into the formula;

q = √(0.1385/8.99 x 10⁹) x 0.046

q = √(1.54060 x 10⁻¹²) x 0.046

q = 7.08 x 10⁻⁸

Take note that 1 nC = 1 x 10⁻⁹ C

Charge, q = 7.08nc

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The kinetic energy at the lowest point is 1.96 Joule. The result is obtained by using the concept of Conservation of mechanical energy.

The Conservation of mechanical energy states that the total mechanical energy of a system is conserved. It can be expressed as

E initial = E final

KE₁ + U₁ = KE₂ + U₂

½mv₁ + mgh₁ = ½mv₂ + mgh₂

Where

The index 1 and 2 shows at point 1 (initial) and 2 (final).

A pendulum that consists of

At its lowest point, find kinetic energy!

The lowest point is at the mean position where h = 0.

Let's say, point 1 is at the highest point and point 2 is at the lowest point.

E initial = E final

½mv₁ + mgh₁ = ½mv₂ + mgh₂

At the highest, the speed is zero. h max means highest position. It would be

½m(0) + mgh₁ = ½mv₂ + mg(0)

mgh₁ = ½mv₂

U₁ = KE₂

The kinetic energy is

KE₂ = mgh₁

KE₂ = 2 (9.8) (0.1)

KE₂ = 1.96 Joule

Hence, the kinetic energy at the lowest point is 1.96 Joule.

The correct option is (G).

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Since the sum of the odd term coefficients and the even term coefficients must both be zero, the expression a0+a1k+a2k2++ankn is divisible by 3 for all kN.

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Each sort of atom in an element is unique. The joining of two or more distinct atoms results in a compound. In a mixture, two or more distinct substances are combined but not chemically bonded.

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Answer:40 miles/hour

The internal torque acting at point C is 800 lb-ft clockwise, and at point D is  1500 ft-lb anti-clockwise.

The shaft is bearing at a and b. As the shaft is at rest and not rotating in any direction. So the internal torque must be balancing the external torques acting on the shaft. Near the bearing A, the the external torque acting on the shaft is 1500 lb-ft clockwise, so at point D there must be an anti-clockwise torque. So the torque acting on the D is 1500 ft-lb.

Similarly, near the bearing B the external torque acting on the shaft is 800 lb-ft anti-clockwise, so there must be an equal and external clockwise torque working on point C to balance the 800 anti-clockwise torque. So the internal torque working on point C is 800 lb-ft.

--The given question is incomplete, the complete question is:

"the support bearings at a and b allow free turning of the shaft. (figure 1) figure1 of 1 part a determine the resultant internal torque acting on the cross section at points c and d . enter your answers in newton-meters to three significant figures separated by a comma."

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(a) The change in the length of the bar is 0.012 m.

(b) The new length of the bar is 10.012 m.

The change in the length of the bar is calculated by applying the following formula.

ΔL = αLΔθ

where;

ΔL = ( 24 x 10⁻⁶ x 10) x ( 40 - -10)

ΔL =  ( 24 x 10⁻⁶ x 10) x ( 50)

ΔL = 0.012 m

The new length of the bar is calculated as follows;

L₁ = L + ΔL

L₁ = 10 m + 0.012 m

L₁ = 10.012 m

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The final velocity of the two objects is 4.8m/s.

What does the word "velocity" mean?

The displacement that an object or particle experiences with respect to time is expressed vectorially as velocity. The meter per second (m/s) is the accepted unit of velocity magnitude (also known as speed). Alternately, the magnitude of velocity can be expressed in centimeters per second (cm/s).

The change in velocity between the objects following a collision is known as the relative velocity. When particles collide, momentum and energy are transferred, which results in a change in velocity. It abides under the rule of conservation of energy and momentum.

m1 = 75kg

m2 = 75+315kg = 390kg

v1 = 25m/s

v2 = ?

Initial momentum = m1*v1

Final momentum = m2*v2

Initial momentum = Final momentum

m1v1 = m2v2

75*25 = 390 *v2

v2 = 75*25/390

v2 = 4.8m/s

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The change in the momentum is equal to the product of the mass and the change in the velocity.

what is change in momentum?

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a) The speed of the 60 Kg ball is  4.1 m/s

b) The KE before and after collision is  144 J and 64 J respectively

c) The KE lost is 80 J

We know that when we talk about the momentum, our minds would go to the collision of the objects that we have in this case which are the balls in the question.

a) Momentum before collision = Momentum after Collison

(2 * 12) + (4 * 60) = (8 * 2) + (60 * v)

v is the velocity of the 60Kg ball

24 + 240 = 16 + 60v

v = 4.1 m/s

b) KE before collision

1) 0.5 * 2 * (12)^2 = 144 J

2) 0.5 * 60 * 4^2 = 480 J

KE after collision;

1) 0.5 * 2 * 8^2 = 64 J

2) 0.5 * 60 * (4.1)^2 = 504.3 J

c) The KE lost in the collision is; 144 J - 64 J = 80 J

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The line 1-0+t2 in relation to the plane x-2y+z =1 is parallel to the plane as both points satisfy the plane equation.

A plane is a two-dimensional, Euclidean surface which never ends in the mathematics. A plane is a point's (zero dimensions), a line's (one dimensions), and space's (three dimensions) two-dimensional equivalents.

A line is a network of interconnected points that can go on forever in both the directions. Three noncollinear points, two parallel lines, or two intersecting lines can all be used to form a plane. If two points are on the same line, they are said to be collinear.

The question is incomplete, find the complete question here

which of the following is true about the line 1-0+t2 in relation to the plane x-2y+z =1 ? group of answer choices

the line lies on the plane.

the line intersects the plane in one point.

the line is parallel to the plane.

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Multiplying the number of work-days (people-days) in an iteration by the velocity is necessary in order to calculate the amount of work that can be completed in an iteration.

Iteration is a process in which a sequence of actions or steps is repeated to achieve an intended outcome. It is an efficient programming practice that helps to simplify complex tasks and achieve desired results. Iteration is also known as looping and is an integral part of computer programming. Iteration helps to repeat a set of instructions until a certain condition is met, saving time and effort. It is a powerful tool that can be used to solve complex problems and create efficient algorithms.

The velocity is a measure of how much work can be completed by a team in a given time frame, and thus multiplying it by the number of work-days in an iteration gives an indication of the total amount of work that can be completed in that iteration. This helps teams plan their work and set realistic expectations for what can be accomplished in a given iteration.

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The speed of the bowling ball is 2.4 m/s forward.

The speed of the bowling ball is calculated by applying the principle of conservation of linear momentum as shown below.

P1 = -P2

where;

P1 = -mv

-P1 = mv

where;

The speed of the bowling ball is calculated as;

v = ( - 12 kgm/s ) / ( 5 kg )

v = -2.4 m/s

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The magnitude of the acceleration of the outside wall the instant before it reaches maximum speed is 948 ft/s^2.

Acceleration is the rate of change of velocity over time. It is the increase in speed or the decrease in the time taken to cover a particular distance.

The equation describing the velocity of the outside wall of the washer is a linear one, given by the equation:
v(t) = at
where a is the acceleration of the wall and t is the time.
We know that the velocity of the wall when it reaches maximum speed is 4 revolutions per second. We can convert this to linear velocity by multiplying it by the circumference of the washer, 2πr, where r is the radius of the washer (1.5 feet). This gives us a final velocity of 9π ft/s
We can now solve for the acceleration of the wall. We know the final velocity and we can set the initial velocity to 0 due to the fact that the washer is starting from rest. So we can solve for the acceleration using the equation:
a = v(t) / t
Plugging in our values, we get:
a = 9π ft/s / t
Now we can solve for the time it takes to get the washer to maximum speed. We know that the final velocity is 9π ft/s and the acceleration is a. So we can solve for the time by rearranging the equation to get:
t = v(t) / a
Plugging in our values, we get:
t = 9π ft/s / a
Solving for t, we get:
t = 9π ft/s / 948 ft/s^2
Simplifying, we get:
t = 7.54 s
Therefore, it takes 7.54 seconds for the washer to reach its maximum speed. The magnitude of the acceleration of the outside wall the instant before it reaches maximum speed is 948 ft/s^2.

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The distance travelled by the object between 5 and 10 seconds is 25 m.

The area under velocity time graph gives the distance travelled by the object.

The distance travelled by the object between 5 and 10 seconds is calculated from the area of curve within this time range.

Area of the curve between 5 and 10 seconds = Area of triangle

Distance travelled between 5 and 10 seconds = Area of triangle formed between 5 and 10 seconds

Area of triangle = ¹/₂bh

where;

A = ¹/₂ x (10 - 5 ) x ( 10 )

A = 25 m

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1. The net force is 79.1°

The angle between those two forces is 120 degrees (because the triangle is equilateral) so the net force on particle 3 is the vector sum of the two forces.

The direction of the force on particle 3 due to particle 1 is along the line joining particles 1 and 3. The direction of the force on particle 3 due to particle 2 is along the line joining particles 2 and 3.

To find the net electric force acting on particle 3 due to particles 1 and 2, we can use Coulomb's law, which states that the force between two point charges is given by the equation:

[tex]F = k * (q1 * q2) / r^2[/tex]

where F is the force, k is the Coulomb constant [tex](8.99 x 10^9 N * m^2/C^2)[/tex], q1 and q2 are the charges of the two particles, and r is the distance between the two particles.

In this case, we have three particles placed at the corners of an equilateral triangle, with a side length of 3.1 cm. Since the triangle is equilateral, all three sides are equal in length, so r1 = r2 = 3.1 cm

The net force on particle 3 is the vector sum of the two forces acting on it due to particles 1 and 2.

F3 = F31 + F32 where F31 is the force on particle 3 due to particle 1 and F32 is the force on particle 3 due to particle 2

[tex]F31 = k * (q3 * q1) / r1^2[/tex]

[tex]F32 = k * (q3 * q2) / r2^2[/tex]

[tex]F31 = 8.99 x 10^9 N * m^2/C^2 * (8.0 nC * -8.4 nC) / (3.1 cm)^2[/tex]

[tex]F32 = 8.99 x 10^9 N * m^2/C^2 * (8.0 nC * -16.8 nC) / (3.1 cm)^2[/tex]

[tex]F31 = -9.52 * 10^{-4 N}[/tex]

[tex]F32 = -1.93 * 10^{-3 N}[/tex]

[tex]F3 = F31 + F32 = -2.88 * 10^{-3 N}[/tex]

After solving, The net force = 79.1°

The direction of the force on particle 3 due to particle 1 is along the line joining particles 1 and 3. The direction of the force on particle 3 due to particle 2 is along the line joining particles 2 and 3.

The angle between those two forces is 120 degrees (because the triangle is equilateral) so the net force on particle 3 is the vector sum of the two forces

2. Particle 3 will move in the direction of the net force acting on it, which is the vector sum of the two forces acting on it due to particles 1 and 2.

Since the net force is [tex]-2.88 * 10^{-3 N}[/tex], and the angle between the direction of the forces on particle 3 due to particles 1 and 2 is 120 degrees, particle 3 will move in the direction of the angle bisector of the angle between those two forces.

The angle bisector of 120 degrees is 60 degrees, thus the net force is acting on particle 3 at 60 degrees with respect to the positive x-axis.

The instant after being released, particle 3 will move in the direction of the net force vector and it will have a velocity vector pointing in the same direction as the net force.

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The magnitude of the n.et force on particle B due to the other two particles is  8 x 10¹⁹ N

The net force on particle B due to the other two particles is calculated by applying the formula for electric force.

F = ( kq₁q₂) / r²

where;

Electric force between A and B;

F(AB) = ( 9 x 10⁹ x 10 x 10⁻⁴ x 6.1 x 10⁴ ) / ( 0.73² )

F (AB) = 1.03  x 10¹² N

Electric force between B and C;

F(BC) = ( 9 x 10⁹ x 17.3 x 10⁴ x 6.1 x 10⁴ ) / ( 1.09² )

F (BC) = 8 x 10¹⁹ N

The net force on particle B is calculated as;

F (net) = - F (AB) - F (BC)

F (net) = - 1.03  x 10¹² N  -  8 x 10¹⁹ N

F (net) = -  8 x 10¹⁹ N

F (net) =  8 x 10¹⁹ N towards A

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The fundamental units of charge is 14.18 C for moving 22.7C of charge.

An object's ability to feel an attractive or repulsive force toward another is determined by its electric charge, also known as charge for short. The coulomb is the primary measure of charge (C). There are two forms of charge: protons exhibit positive charge, while electrons exhibit negative charge (exhibited by electrons). The electric forces between charged particles are described by Coulomb's law; if the charges shift, the electromagnetic force becomes more complex.

fundamental charge=[tex]\frac{q}{e}[/tex]

Now, n=[tex]\frac{22.7}{1.6\times10^{-19} }[/tex]

n=[tex]1.418\times10^{20}[/tex]

and according to question,

the value of fundamental unit charge is 14.18.

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10.628 kW of power must the winch motor provides when the car is moving at constant speed at the slope of 30.0o at a speed of 2.20m/s for 12 s to keep of moving.

The maximum Force, with the maximum speed of the motor, gives maximum power Now we know

a = (vf-vi)/t = (2.20 - 0)/12 => 0.1853 m/s^2

The maximum force is when the car is accelerating so,

f = fa+fg

F = ma+ ma * sign 30o => 4831.035 N ( As  shown in the Image attached how the perpendicular vector that is a signθ is taken)

So the force will be 4831.035 N

Hence the maximum power p = fxV

4831.035 * 2.20

P =10626.27 w

which results in 10626.27/1000 kW

So 10.628 Kw is the maximum power required for the slop of 30o.

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The correct statement is:

"The magnitude of the acceleration of object A is 6 times less than the magnitude of the acceleration of object B"

The magnitude of the acceleration for an object can be calculated using Coulomb's law, which states that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. The formula for the force between two charges is:

F = (k * q1 * q2) / r^2

where F is the force, k is the Coulomb constant, q1 and q2 are the charges, and r is the distance between the charges.

Since the acceleration is the force divided by the mass, we can use the formula:

a = F / m

where a is the acceleration, F is the force, and m is the mass.

Given that the charge on object A is 3 times higher than on object B, and object A has a 6 times higher mass than object B, we can determine that:

The force acting on object A is 3 times greater than the force acting on object B (due to the difference in charges)

The mass of object A is 6 times greater than the mass of object B

So, the acceleration of object A is 6 times less than the acceleration of object B.

Therefore, the correct statement is:

"The magnitude of the acceleration of object A is 6 times less than the magnitude of the acceleration of object B"

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The answer is B. 2 s. The impulse provided by both engines is the same, so they must fire for the same amount of time in order to provide that amount of impulse.

Engines are devices that convert energy into mechanical force, usually to power machines and vehicles. Engines come in a variety of forms and sizes, but all are based on the same basic principles of converting thermal energy into mechanical force via combustion.

Since the first engine fires for 2 s and provides 6 N of thrust,
the second engine must also fire for 2 s to provide 4 N of thrust (since 6N/2s = 4N/x, where x = 2s).

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