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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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8 0
3 years ago
An electric dipole consisting of charges of magnitude 1.70 nC separated by 6.80 μm is in an electric field of strength 1160 N/C.
bazaltina [42]

Answer:

p = 1.16 10⁻¹⁴ C m     and  ΔU = 2.7 10 -11 J

Explanation:

The dipole moment of a dipole is the product of charges by distance

                        p = 2 a q

With 2a the distance between the charges and the magnitude of the charges

                        p = 1.7 10⁻⁹ 6.8 10⁻⁶

                        p = 1.16 10⁻¹⁴ C m

 

The potential energie dipole  is described by the expression

                       U = - p E cos θ

Where θ is the angle between the dipole and the electric field, the zero value of the potential energy is located for when the dipole is perpendicular to the electric field line

Orientation parallel to the field

                      θ = 0º

                      U = 1.16 10⁻¹⁴ 1160 cos 0

                      U1 = 1.35 10⁻¹¹ J

Antiparallel orientation

                       θ = 180º

                      cos 180 = -1

                      U2 = -1.35 10⁻¹¹ J

The difference in energy between these two configurations is the subtraction of the energies

                         ΔU = | U1 -U2 |

                         ΔU = 1.35 10-11 - (-1.35 10-11)

                         ΔU = 2.7 10 -11 J

6 0
3 years ago
"A steel rotating-beam test specimen has an ultimate strength of 120 kpsi. Estimate the life of the specimen if it is tested at
MrRissso [65]

Answer:

life (N) of the specimen is 117000  cycles

Explanation:

given data

ultimate strength Su = 120 kpsi

stress amplitude σa = 70 kpsi

solution

we first calculate the endurance limit of specimen Se i.e

Se = 0.5× Su   .............1

Se = 0.5 × 120

Se = 60 kpsi

and we know strength of friction f  = 0.82

and we take endurance limit Se is = 60 kpsi

so here coefficient value (a) will be

a = \frac{(f\times Su)^2}{Se}     ......................1  

put here value and we get

a = \frac{(0.82\times 120)^2}{60}  

a = 161.4  kpsi

so coefficient value (b) will be

b = -\frac{1}{3}log\frac{(f\times Su)}{Se}  

b =  -\frac{1}{3}log\frac{(0.82\times 120)}{60}  

b = −0.0716

so here number of cycle N will be  

N =  (\frac{ \sigma a}{a})^{1/b}

put here value  and we get

N =  (\frac{ 70}{161.4})^{1/-0.0716}

N = 117000

so life (N) of the specimen is 117000  cycles

7 0
3 years ago
Is electrical conductivity?
expeople1 [14]

Answer:

can't tell if this is question, it is not written correctly

Explanation:

Electrical conductivity is the measure of a material's ability to allow the transport of an electric charge. Its SI is the siemens per meter, (A2s3m−3kg−1) (named after Werner von Siemens) or, more simply, Sm−1. It is the ratio of the current density to the electric field strength.

8 0
3 years ago
Solve for the unknown in each of these circuits
Tamiku [17]

<u> Ohms law: </u> This law relates voltage difference between two points. Mathematically, the law states that V=IR;

                Where

                          V = voltage difference ; in volts

                          I = Current ; in Amperes

                          R = Resistance ; in ohms

<u>1. Answer : </u> given that R = 10 ; V= 12 V ;  I = ?

From ohms law,    I = V/R

                                = 12/10

                                = 1.2 Amp.

<u>2. Answer:</u>  given that R = 10 ; V= ? ;  I = 5

From ohms law,    V = IR

                                 = 10×5 = 50 V

<u>3 . Answer:</u>  given that R = ? ; V= 120 ;  I = 5

From ohms law,    R =  V/I

                                 = 120/5

                                 = 24 Ω

<u>4 . Answer:</u>  given that R = ? ; V= 10 ;  I = 20

From ohms law,    R =  V/I

                                 = 10/20

                                 = 0.5 Ω

<u>5 . Answer:</u>  given that R = 480 ; V= 24 ;  I = ?

From ohms law,  I =  V/R

                              = 24/480

                              = 0.05 A

<u>6. Answer:</u>  given that R = 150 ; V= ? ;  I = 1

From ohms law,  V = IR

                               = 1 × 150

                               = 150 V


6 0
3 years ago
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