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The position vector is given by vector r= 5t² I cap + 2 t³ j cap + 2 k cap. Find it's velocity and acceleration at t=2s.

Answer: C

Explanation: It's a lot of math.

The option that gives the correct value for the angle theta above the horizontal axis of the velocity of the body, v is option C.

C. 53.1°

The given parameters are;

The velocity of the body relative to the horizontal axis, vₓ = 6 m/s

The velocity of the body relative to the vertical axis, [tex]v_y[/tex] = 8 m/s

Required;

The measure of the angle theta above above the horizontal axis of the velocity of the body, v

Solution:

The velocity of the body can be represented vectorially as follows;

v = 6·i + 8·j

The vectoral form gives the legs of the right triangle that has the magnitude and direction as the hypotenuse side

Therefore;

[tex]\theta = arctan \left(\dfrac{8}{6} \right) \approx \underline{53.1^{\circ}}[/tex]

Learn more about the vectors here:

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Answer:

the photo is a bit blur

Answer:

10N

Explanation:

Applying the Hooke law:

F = kx

F: Force

k: stiffness coefficient

x: stretched distance

F = 10N/m x 1m = 10N

Answer:

* if the spring force is greater than the maximum of the static friction force,  

               Fe = m (a + μ_k g)

* If the elastic force is less than or equal to the static friction force, the result is with static friction coefficient

              Fe =μ_s m g

Explanation:

For this exercise we must apply Newton's second law to the system

X axis

         Fe -fr = m a

         Fe = m a + fr

Y axis  

        N-W = 0

        N = W = mg

the roe force is given by

        fr = μ N

        fr = μ mg

we substitute

      Fe = m a + μ m g

      Ee = m (a + μ g)

Let's analyze the solution. We have several possibilities

* if the spring force is greater than the maximum of the static friction force, the system acquires an acceleration and the result is with the kinetic friction coefficient

               Fe = m (a + μ_k g)

* If the elastic force is less than or equal to the static friction force, the result is with static friction coefficient

              Fe =μ_s m g

Answer:

K.E of truck > K.E of car

Explanation:

Mass of the truck = 8000Kg

K.E=[tex]\frac{1}{2} mv[/tex]

K.E =[tex]\frac{1}{2}*8000*v\\ 4000v[/tex]

Mass of the car = 1000 Kg

K.E of the car =[tex]\frac{1}{2}*1000*v\\ 500v[/tex]

Therefore Kinetic energy of the truck is greater than that of the car

Answer:

Wholesale Market. 1. The market for the sale of goods to a retailer. That is, a wholesaler receives large quantities of goods from a manufacturer and distributes them to stores, where they are sold to consumers. ... The market for the sale of securities to institutional investors rather than individuals.

Answer:

22.2 m/s or 80 km/h

Explanation:

Given that

Distance travelled by the car, d = 240 km

Time taken by the car, t = 3 hours.

Speed of the car, v = ? m/s

for easy calculations, we will be converting the units to meters and seconds respectively.

240 km to meters would be

240 * 1000 m = 240000 m

3 hrs to seconds would be

3 * 60 mins * 60 seconds = 10800 s

now, we have our distance and time to be

d = 240000 m

t = 10800 s

speed is defined as the ratio of distance with respect to time taken, effectively,

Speed = distance/time

speed, v= 240000 / 10800

v = 22.2 m/s

therefore, the speed of the car during the time is 22.2 m/s, or if the speed is needed in km/h, we can convert it

22.2 * 3600/1000 =

80 km/h

Answer:

the final statements the correct one is. The second

The iron piece exerts a force of 1 N on the magnet in the opposite direction

Explanation:

In this exercise they give us the force exerted by a magnet on an iron bar and ask us the force that the iron bar exerts on the magnet. We can see that these are action and reaction forces, which by Newton's third law must be of equal magnitude and opposite direction, each applied to one of the bodies.

the final statements the correct one is. The second

The iron piece exerts a force of 1 N on the magnet in the opposite direction

Answer:

a business who buys goods and services

Answer:

(II). The fractions in simplest form

[tex]\dfrac{31}{35}[/tex], [tex]\dfrac{91}{165}[/tex] and [tex]\dfrac{13}{5}[/tex]

(III). The fractions in ascending order

[tex]\dfrac{91}{165}<\dfrac{31}{35}<\dfrac{13}{5}[/tex]

Explanation:

Given that,

(I). Represent the fractions in pictorial form

(II). Write the fractions in simplest form.

(III). Arrange them in ascending order.

Suppose, The fractions in pictorial form

(a). [tex]\dfrac{3}{5}+\dfrac{2}{7}[/tex]

(b). [tex]\dfrac{9}{11}-\dfrac{4}{15}[/tex]

(c). [tex]\dfrac{7}{10}+\dfrac{2}{5}+\dfrac{3}{2}[/tex]

We need to write in simplest form

Using given fraction

(a). [tex]\dfrac{3}{5}+\dfrac{2}{7}=\dfrac{3\times7}{5\times7}+\dfrac{2\times5}{7\times5}[/tex]

[tex]\dfrac{3}{5}+\dfrac{2}{7}=\dfrac{21}{35}+\dfrac{10}{35}[/tex]

[tex]\dfrac{3}{5}+\dfrac{2}{7}=\dfrac{21+10}{35}[/tex]

[tex]\dfrac{3}{5}+\dfrac{2}{7}=\dfrac{31}{35}[/tex]

(b). [tex]\dfrac{9}{11}-\dfrac{4}{15}=\dfrac{9\times15}{11\times15}-\dfrac{4\times11}{15\times11}[/tex]

[tex]\dfrac{9}{11}-\dfrac{4}{15}=\dfrac{135-44}{165}[/tex]

[tex]\dfrac{9}{11}-\dfrac{4}{15}=\dfrac{91}{165}[/tex]

(c). [tex]\dfrac{7}{10}+\dfrac{2}{5}+\dfrac{3}{2}=\dfrac{7}{10}+\dfrac{2\times2}{5\times2}+\dfrac{3\times5}{5\times2}[/tex]

[tex]\dfrac{7}{10}+\dfrac{2}{5}+\dfrac{3}{2}=\dfrac{7}{10}+\dfrac{4+15}{10}[/tex]

[tex]\dfrac{7}{10}+\dfrac{2}{5}+\dfrac{3}{2}=\dfrac{7+4+15}{10}[/tex]

[tex]\dfrac{7}{10}+\dfrac{2}{5}+\dfrac{3}{2}=\dfrac{26}{10}[/tex]

[tex]\dfrac{7}{10}+\dfrac{2}{5}+\dfrac{3}{2}=\dfrac{13}{5}[/tex]

We need to arrange them in ascending order

Using simplest form

The simplest fraction in ascending order

[tex]\dfrac{91}{165}<\dfrac{31}{35}<\dfrac{13}{5}[/tex]

Hence, This is required solution.

Answer:

speed

Explanation:

Explanation:

It is given that,

The Displacement x of particle moving in one dimension under the action of constant force is related to the time by equation as:

[tex]x=4t^3+3t^2-5t+2[/tex]

Where,

x is in meters and t is in sec

We know that,

Velocity,

[tex]v=\dfrac{dx}{dt}\\\\v=\dfrac{d(4t^3+3t^2-5t+2)}{dt}\\\\v=12t^2+6t-5[/tex]

(a) i. t = 2 s

[tex]v=12(2)^2+6(2)-5=55\ m/s[/tex]

At t = 4 s

[tex]v=12(4)^2+6(4)-5=211\ m/s[/tex]

(b) Acceleration,

[tex]a=\dfrac{dv}{dt}\\\\a=\dfrac{d(12t^2+6t-5)}{dt}\\\\a=24t+6[/tex]

Pu t = 3 s in above equation

So,

[tex]a=24(3)+6\\\\a=78\ m/s^2[/tex]

Hence, (a) (i) v = 55 m/s (ii) v = 211 m/s and (b) 78 m/s²

Answer:

a) La magnitud del desplazamiento es de 5 m

La magnitud de la fuerza es 20 N

b) El trabajo realizado por la fuerza es de 100 J

c) El ángulo entre la fuerza y el plano es 0 °

Explanation:

a) La magnitud del desplazamiento se encuentra por la relación;

[tex]\left | X \right | = \sqrt{X_{x}^{2}+X_{y}^{2}}[/tex]

Lo que da;

[tex]\left | X \right | = \sqrt{4^{2}+3^{2}} = 5 \ m[/tex]

De manera similar, la magnitud de la fuerza, F, se encuentra como sigue;

[tex]\left | F \right | = \sqrt{F_{x}^{2}+F_{y}^{2}}[/tex]

Lo que da;

[tex]\left | F \right | = \sqrt{16^{2}+12^{2}} = 20 \ N[/tex]

b) El trabajo, W, realizado por la fuerza = Fuerza, F × Distancia, X

∴ Ancho = 20 N × 5 m = 100 N · m = 100 J

c) La dirección de la fuerza viene dada por la siguiente fórmula;

[tex]tan^{-1} \left (\dfrac{F_y}{F_x} \right ) = tan^{-1} \left (\dfrac{12}{16} \right ) = 38.9^{\circ}[/tex]

La dirección del plano viene dada por la siguiente fórmula;

[tex]tan^{-1} \left (\dfrac{X_y}{X_x} \right ) = tan^{-1} \left (\dfrac{3}{4} \right ) = 38.9^{\circ}[/tex]

Por tanto, el ángulo entre la fuerza y el plano = 0 °

La fuerza actúa a lo largo del plano.

Answer:

In order to be in translational equilibrium, the net force (sum of the forces) must be 0.

Answer:

mechanical energy or chemical energy

Answer:

1. Urea,                    (d)Fertilizer

2. Combines,          (c) Harvesting and threshing

3. Silos,                   (b) Storage of grains

4. Seed drills,          (a) Sowing seeds

5. Irrigation,             (f) Sprinklers

6. Tilling,                  (e) Preparation of soil

Explanation:

1) Urea is a widely used and important fertilizer in the agricultural industry

2) The combine harvester combines three categories of harvesting grain drops such as threshing reaping and winnowing

3) Silos are used to store grains

4) A seed drill is a seed planting mechanism for burying seeds to a particular depth during seed planting

5) Irrigation is the application of required volume of water to plants

6) Tilling is the digging, turning, and staring operations meant to prepare the soil.

Answer:

585×10⁸ m

Explanation:

Distance = rate × time

d = (2.998×10⁸ m/s) (3.25 min) (60 s/min)

d = 585×10⁸ m

Answer:

0.4 N

Explanation:

The weight mg is 8 N, so the mass is:

mg = 8 N

m = 8 N / g

m = 8 N / (10 m/s²)

m = 0.8 kg

The force needed to accelerate it to 0.5 m/s².

F = ma

F = (0.8 kg) (0.5 m/s²)

F = 0.4 N

Answer:

1.) Sowing

2.) Respiration

3.) Soil preparation or cultivation or ploughing

4.) Fertility

5.) 2, 4 -D

6.) winnowing threshers

7.) Surface irrigation and sprinkler irrigation

8.) Weeds

9.) Transplantation

10.) Aeration

Explanation:

1.) Seed drill sows crop seed

2.) Ploughing assist in the respiration and penetration of the roots of a growing plants

3.) Tilling the soil is breaking of the soil lumps and turning of the soil

4.) Manure and fertilizers supply nutrient to the soil for the uptake by plant in food production

5.) 2, 4 -D are a range of weedicide containing 2,4-D as the active ingredient

6.) Winnowing is the separation of grain from straw

Threshers remove seeds from husks and stalks

7.) Surface irrigation -gravity enables the flow of the water

and sprinkler irrigation- Use of preset tools for irrigation

8.) Weeds are the unwanted, in situ, growing plants close to the crops

9.) Transplantation is the method of relocating plants

10.) Excess water limits access of the roots and seeds to atmospheric oxygen

Answer:

27.336

Explanation:

The atomic mass is the weighted average of the atomic masses of the isotopes.  Simply multiply each isotopes's atomic mass by its relative abundance, then sum the results.

m = 0.8233 × 26.975 + 0.1767 × 29.018

m = 27.336

Answer:

Concave mirror makes someone looking at it look dwarf or short, while convex mirror stretches the person making the person look weird.

Answer:

12.3 m/s

Explanation:

The Doppler equation describes how sound frequency depends on relative velocities:

fr = fs (c + vr)/(c + vs),

where fr is the frequency heard by the receiver,

fs is the frequency emitted at the source,

c is the speed of sound,

vr is the velocity of the receiver,

and vs is the velocity of the source.

Note: vr is positive if the receiver is moving towards the source, negative if away.

Conversely, vs is positive if the receiver is moving away from the source, and negative if towards.

Given:

fs = 894 Hz

fr = 926 Hz

c = 343 m/s

vs = 0 m/s

Find: vr

926 = 894 (343 + vr) / (343 + 0)

vr = 12.3

The speed of the car is 12.3 m/s.

Answer:

kinetic energy is 1/2mv^2.

which is 1/2×0.05×3^2

1/2×0.05×9.

1/2×0.45=

0.45÷2=0.225~0.23J

Answer:

3.33 N

Explanation:

First, find the acceleration.

Given:

Δx = 3 m

v₀ = 0 m/s

t = 3 s

Find: a

Δx = v₀ t + ½ at²

3 m = (0 m/s) (3 s) + ½ a (3 s)²

a = ⅔ m/s²

Use Newton's second law to find the force.

F = ma

F = (5 kg) (⅔ m/s²)

F ≈ 3.33 N

Answer:

Explanation:

Initial velocity (u) of the Bullet = 400 m/sec

Final velocity (v) of the Bullet = 100 m/sec

Bullet passed through the block in (t) = 0.0004 sec  

Using 1st Equation of motion :

400 m/s = 100 m/s - a (0.0004)

Deceleration of Bullet = 750,000 m/sec^2

(a) F (force exerted by the wooden block on the bullet) = F (force exerted by the bullet on the wooden block)

F = m * a = 0.008 * 750,000 = 6000 N

(b) Using 3rd Equation of motion :

[tex]v^{2} = u^{2} - 2aS[/tex]

10000 = 160000 - 2 * 750,000 * S

Thickness of wood (S) = 0.1 m

Answer:

0.66*10^-6m

Explanation:

We know that the bright fringes are placed on the screen as follows

Ym= m*(lambda xL/d)

But we are given

L= 5.05

Deta Y= 1.59

d = 0.21

1.59* 10^-2m= lambda * 5.05m/2.1*10^-4m

So lambda=

1.59* 10^-2m x 2.1*10^-4m/ 5.05m

= 0.66*10^-6m

Answer: √(L/g)

Explanation:

Here we only work with the units:

The unit of the period is units of time, so we have:

[T] = [s]

Now, the units of the length of the pendulum are units of distance:

[L] = [m]

And the units of the acceleration are:

[g] = [m/s^2]

Now, we want to work with those two in such way that the end result is only in seconds.

First, we can see that in g we have seconds square, so we know that we should use a square root.

Then we can divide L by g in order to remove the distance unit, and to have the time unit in the numerator

[L/g] = [m*s^2/m] = [s^2]

Now we apply the square root:

[√(L/g)] = [√s^2] = [s]

Then the combination is: √(L/g)

T = k*√(L/g)

where k is the constant of proportionality.

Answer:

find the sum of the inital and final velocitys and divide by 2 to find the average

The answer is 65.3 inches tall

Explanation:

To know the heigh of Sammy in inches it is necessary to convert the 5 feet to inches and add this number to 5.3 inches as the statement mentions "Sammy is 5 feet and 5.3 inches tall". Additionally, it is known each foot is equal to 12 inches ( 1 foot = 12 inches). According to this, the simplest method to convert feet to inches is to multiply the feet given by 12. The process is shown below:

1 foot  = 12 inches

feet to inches =  number of feet x 12

5 feet x 12 = 60 inches

This means 5 feet is equal to 60 inches. Now, 60 inches + 5.3 inches = 65.3 inches (total height of Sammy in inches)

Answer:

The new Coulomb force is q₁q₂/9πε₀r²

Explanation

The coulomb force between the two charges q₁ and q₂ at a distance r in air is given by F = q₁q₂/4πε₀r².

Now, let us assume the material of dielectric constant κ = 9 is placed between them on the side of the q₁ charge. The value of its effective charge is now q₃ = q₁/κ at a distance of d = r/2 from the q₂ charge.

Since we have air between q₂ and q₃, the coulomb force between them is

F' = q₂q₃/4πε₀d²

= q₂(q₁/κ)/4πε₀(r/2)²

=  4q₂q₁/κ4πε₀r²

= 4/κ(q₂q₁/4πε₀r²)

= 4/9 × (q₂q₁/4πε₀r²)

= q₁q₂/9πε₀r²

So, the new Coulomb force is q₁q₂/9πε₀r²