Move numbers to the boxes to show the factor pairs of 14. Response area with 4 blank spaces Blank space 1 empty times Blank space 2 empty equals 14 Blank space 3 empty times Blank space 4 empty equals 14 Answer options with 14 options. Answer Options 1 2 3 4 5 6 7 8 9 10 11 12 13 1

The magnitude of the resultant vector is obtained by finding the sum of two horizontal vectors and the sum of two vertical vectors. Thus, option C is correct.

The resultant vector is the single vector that has the same effect in the number of vectors collectively produced. The resultant vector in the horizontal and vertical direction is obtained by drawing a diagonal and hence by using the Pythagoras theorem.

To find resultant vector is obtained by finding the sum of two horizontal vectors and vertical vectors and then using the Pythagoras theorem.

Thus, the ideal solution is option C.

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a. To find the acceleration, we can use the equation:

acceleration = change in velocity / time taken

Here, the initial velocity is 0 m/s (since she starts from rest), the final velocity is 5 m/s, and the time taken is 10 s. Therefore:

acceleration = (5 m/s - 0 m/s) / 10 s = 0.5 m/s^2

So the acceleration of the girl on her bicycle is 0.5 m/s^2.

b. The average speed during the 10 s can be found by dividing the total distance traveled by the time taken. We don't know the distance traveled yet, so we can use another equation:

distance = (initial velocity x time taken) + (0.5 x acceleration x time taken^2)

Here, the initial velocity is 0 m/s, and the time taken is 10 s. We already calculated the acceleration in part (a) as 0.5 m/s^2. Plugging these values in, we get:

distance = (0 m/s x 10 s) + (0.5 x 0.5 m/s^2 x (10 s)^2) = 25 meters

So the girl traveled 25 meters in 10 seconds.

c. As the girl pedals, she applies force to the pedals, which in turn transfers the force to the rear wheel. This force drives the bicycle forward, causing it to gain speed. However, when the bicycle picks up speed, air resistance (also called drag) comes into play, which increases. Eventually, the force of air resistance becomes equal and opposite to the force that propels the bicycle forward. This means that the net force on the bicycle becomes zero, stopping its acceleration and reaching its maximum speed, known as the terminal velocity. Even if the girl pedals faster, she won't be able to increase her speed because the drag force counteracts the propelling force.

During Simple Harmonic Motion (SHM), an object at the mean position has potential energy (P.E)=0 and kinetic energy (K.E)=MAX. So, the correct option is (d).

In Simple Harmonic Motion (SHM), an object oscillates about a mean position, with the motion characterized by a restoring force proportional to its displacement from the mean position.

When the object is at the mean position, it has maximum kinetic energy (K.E) because it is at its maximum velocity, and it has zero potential energy (P.E) since it is not displaced from the equilibrium position.

As the object moves further from the mean position, its P.E increases, and K.E decreases. The correct answer to the question is option (d), where P.E=0 and K.E=MAX at the mean position.

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The density of the solid is (4.10 ± 0.78) × 10^3 kg/m^3.

To calculate the density of the cube below formula can be used:

ρ = m/V

where ρ is density, m is mass, and V is volume. For a cube, the volume is given by:

V = (side)^3

Therefore, the uncertainty in density can be calculated using the formula:

δρ/ρ = sqrt[(δm/m)^2 + 3(δs/s)^2]

where δρ is the uncertainty in density, δm is the uncertainty in mass, δs is the uncertainty in side, and s is the value of the side.

Now, putting in the given values:

s = (1.00 ± 0.06) cm = 0.01 ± 0.0006 m

m = (41.0 ± 0.4) g = 0.0410 ± 0.0004 kg

Volume, V = (0.01 m)^3

                  = 1.0 × 10^-6 m^3

Therefore, the density is:

ρ = m/V

  = 0.0410 kg/1.0 × 10^-6 m^3

  = 4.10 × 10^4 kg/m^3

Now substituting the values and calculating the uncertainty in density:

δρ/ρ = sqrt[(δm/m)^2 + 3(δs/s)^2]

δρ/ρ = sqrt[(0.0004/0.0410)^2 + 3(0.0006/0.01)^2]

δρ/ρ = 0.019

Therefore, the uncertainty in density is:

δρ = (0.019)(4.10 × 10^4 kg/m^3)

     = 779 kg/m^3

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The reflection in a clear window of a store is a(n) image.

Images are seen as reflections because of the behavior of light. When light strikes a smooth, reflective surface such as a mirror or still water, it bounces off the surface at the same angle at which it hit it. This process is called reflection. The reflected light rays then travel to our eyes, creating an image.

The angle of incidence (the angle at which the light strikes the surface) is equal to the angle of reflection (the angle at which the light bounces off the surface). This causes the reflected image to be a mirror image of the original object.

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