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Pavel [41]
3 years ago
7

Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x' (t) is its velocity, and x'

' (t) is its acceleration. x(t) = t3 − 12t2 + 21t − 9, 0 ≤ t ≤ 10 (a) Find the velocity and acceleration of the particle.
Physics
1 answer:
nignag [31]3 years ago
5 0

The position of the particle is given by:

x(t) = t³ - 12t² + 21t - 9

Differentiate x(t) with respect to t to find the velocity x'(t):

x'(t) = 3t² - 24t + 21

Differentiate x'(t) with respect to t to find the acceleration x''(t):

x''(t) = 6t - 24

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Astronomers build optical telescopes on tops of mountains because a. there is less air to dim the light. b. the seeing is better
V125BC [204]

Answer: choices a and b

Explanation:

Telescope can be defined as am optical instrument which is designed to observe the distant objects clear and nearer. It comprises of arrangement of lenses which allow the rays of light to be collected. The collected light is focused and the image so produced is magnified in the form of an image. The telescopes are prepared and manufactured on mountains top as this will help in preventing the distortion of light obtain from the star due to the fluctuation of air mass in the atmosphere. The atmospheric distortion affects the resolution, and affects the vision. The atmospheric pressure is low at the mountain tops so it will help in better observation of the sky.

6 0
2 years ago
A block of amber is placed in water and a laser beam travels from the water through the amber. The angle of incidence is 35 degr
7nadin3 [17]
Answer: 1.88

Explanation

Applying Snell’s Law, sin(1)/sin(2) = n(2)/n(1), where n is the index of refraction and sin 1 and 2 being of incidence and refracted respectively.

1) sin35/sin24 = n(2)/1.33
2) 1.41 = n(2)/1.33
3) n(2) = 1.41 x 1.33
4) n(2) = 1.88

Hope this helps :)
7 0
3 years ago
what is the energy (in j) of a photon required to excite an electron from n = 2 to n = 8 in a he⁺ ion? submit an answer to three
grin007 [14]

Answer:

Approximately 5.11 \times 10^{-19}\; {\rm J}.

Explanation:

Since the result needs to be accurate to three significant figures, keep at least four significant figures in the calculations.

Look up the Rydberg constant for hydrogen: R_{\text{H}} \approx 1.0968\times 10^{7}\; {\rm m^{-1}.

Look up the speed of light in vacuum: c \approx 2.9979 \times 10^{8}\; {\rm m \cdot s^{-1}}.

Look up Planck's constant: h \approx 6.6261 \times 10^{-34}\; {\rm J \cdot s}.

Apply the Rydberg formula to find the wavelength \lambda (in vacuum) of the photon in question:

\begin{aligned}\frac{1}{\lambda} &= R_{\text{H}} \, \left(\frac{1}{{n_{1}}^{2}} - \frac{1}{{n_{2}}^{2}}\right)\end{aligned}.

The frequency of that photon would be:

\begin{aligned}f &= \frac{c}{\lambda}\end{aligned}.

Combine this expression with the Rydberg formula to find the frequency of this photon:

\begin{aligned}f &= \frac{c}{\lambda} \\ &= c\, \left(\frac{1}{\lambda}\right) \\ &= c\, \left(R_{\text{H}}\, \left(\frac{1}{{n_{1}}^{2}} - \frac{1}{{n_{2}}^{2}}\right)\right) \\ &\approx (2.9979 \times 10^{8}\; {\rm m \cdot s^{-1}}) \\ &\quad \times (1.0968 \times 10^{7}\; {\rm m^{-1}}) \times \left(\frac{1}{2^{2}} - \frac{1}{8^{2}}\right)\\ &\approx 7.7065 \times 10^{14}\; {\rm s^{-1}} \end{aligned}.

Apply the Einstein-Planck equation to find the energy of this photon:

\begin{aligned}E &= h\, f \\ &\approx (6.6261 \times 10^{-34}\; {\rm J \cdot s}) \times (7.7065 \times 10^{14}\; {\rm s^{-1}) \\ &\approx 5.11 \times 10^{-19}\; {\rm J}\end{aligned}.

(Rounded to three significant figures.)

6 0
2 years ago
using hooke's law, f spring = k triangle x, find the elastic constant of a spring that stretches 2 cm when a 4 newton force is a
Ksivusya [100]

As we know that spring force is given as

F = kx

here we know that

F = 4 N

x = 2 cm = 0.02 m

now from the above equation we will have

4 = k(0.02)

k = 200 N/m

so the elastic constant of the spring will be 200 N/m

8 0
3 years ago
When we look into the sky every day we get to see the results of all the behaviors of waves. The blue color of the sky results f
mr_godi [17]

Answer:

λ = 0.4 x 10⁻⁶ m = 400 nm

Explanation:

The relationship between frequency, wavelength and speed of an electromagnetic wave is given as follows:

c = f\lambda

where,

c = speed of light = 3 x 10⁸ m/s

f = frequency of the light wave = 7.5 x 10¹⁴ Hz

λ = wavelength of the light = ?

Therefore,

3\ x\ 10^8\ m/s = (7.5\ x\ 10^{14}\ Hz)\lambda\\\\\lambda = \frac{3\ x\ 10^8\ m/s}{7.5\ x\ 10^{14}\ Hz}

<u>λ = 0.4 x 10⁻⁶ m = 400 nm</u>

4 0
3 years ago
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