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3 years ago

A car changes speed from 25 m/s to 10 m/s in 240 seconds. Describe its acceleration.

Physics

1 answer:

Dmitry_Shevchenko [17]3 years ago

7 0

Explanation:

Acceleration is change in velocity over change in time:

a = Δv / Δt

a = (10 m/s - 25 m/s) / (240 s - 0 s)

a = -0.0625 m/s²

So the car decelerates at 0.0625 m/s².

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A thin spherical spherical shell of radius R which carried a uniform surface charge density σ. Write an expression for the volum

ozzi

Answer:

Explanation:

From the given information:

We know that the thin spherical shell is on a uniform surface which implies that both the inside and outside the charge of the sphere are equal, Then

The volume charge distribution relates to the radial direction at r = R

∴

$\rho (r) \ \alpha \ \delta (r -R)$

$\rho (r) = k \ \delta (r -R) \ \ at \ \ (r = R)$

$\rho (r) = 0\ \ since \ r< R \ \ or \ \ r>R---- (1)$

To find the constant k, we examine the total charge Q which is:

$Q = \int \rho (r) \ dV = \int \sigma \times dA$

$Q = \int \rho (r) \ dV = \sigma \times4 \pi R^2$

∴

$\int ^{2 \pi}_{0} \int ^{\pi}_{0} \int ^{R}_{0} \rho (r) r^2sin \theta \ dr \ d\theta \ d\phi = \sigma \times 4 \pi R^2$

$\int^{2 \pi}_{0} d \phi* \int ^{\pi}_{0} \ sin \theta d \theta * \int ^{R}_{0} k \delta (r -R) * r^2dr = \sigma \times 4 \pi R^2$

$(2 \pi)(2) * \int ^{R}_{0} k \delta (r -R) * r^2dr = \sigma \times 4 \pi R^2$

Thus;

$k * 4 \pi \int ^{R}_{0} \delta (r -R) * r^2dr = \sigma \times R^2$

$k * \int ^{R}_{0} \delta (r -R) r^2dr = \sigma \times R^2$

$k * R^2= \sigma \times R^2$

$k = R^2 --- (2)$

Hence, from equation (1), if k = $\sigma$

$\mathbf{\rho (r) = \delta* \delta (r -R) \ \ at \ \ (r=R)}$

$\mathbf{\rho (r) =0 \ \ at \ \ rR}$

To verify the units:

$\mathbf{\rho (r) =\sigma \ * \ \delta (r-R)}$

↓ ↓ ↓

c/m³ c/m³ × 1/m

Thus, the units are verified.

The integrated charge Q

$Q = \int \rho (r) \ dV \\ \\ Q = \int ^{2 \ \pi}_{0} \int ^{\pi}_{0} \int ^R_0 \rho (r) \ \ r^2 \ \ sin \theta \ dr \ d\theta \ d \phi \\ \\ Q = \int ^{2 \pi}_{0} \ d \phi \int ^{\pi}_{0} \ sin \theta \int ^R_{0} \rho (r) r^2 \ dr$

$Q = (2 \pi) (2) \int ^R_0 \sigma * \delta (r-R) r^2 \ dr$

$Q = 4 \pi \sigma \int ^R_0 * \delta (r-R) r^2 \ dr$

$Q = 4 \pi \sigma *R^2$ since $( \int ^{xo}_{0} (x -x_o) f(x) \ dx = f(x_o) )$

$\mathbf{Q = 4 \pi R^2 \sigma }$

6 0

3 years ago

The results of a recent television survey of American TV households revealed that 86 out of every 100 TV households have at leas

Lelechka [254]

Answer:

$q = \dfrac{14}{100}$

Explanation:

given,

86 out of every 100 TV households have at least one remote control

Probability of any material is calculated by.

$Probability = \dfrac{favourable\ outcome}{Total\ outcome}$

$P(at\ least\ one\ remote\ control)=\dfrac{86}{100}$

$P(at\ least\ one\ remote\ control)=0.86$

now, Calculating probability that at least one remote control

q = 1 - 0.86

q = 0.14

$P(doesnot\ have\ at\ least\ one\ remote\ control)=\dfrac{14}{100}$

$q = \dfrac{14}{100}$

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3 years ago

How many neutrons are in an atom of Carbon-13 or (613C)?

vivado [14]

Answer: 6 OR 7

Explanation:

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2 years ago

I need help with this

lord [1]

Answer:

0.832

Explanation:

8.320 x 10 to the negative 1st power is 0.832

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3 years ago

Why is honesty especially important in a scientist when the results of an experiment go against predictions❓❔

kramer

Because other scientists and science in general rely on their collegues' research which in turn allows development of our knowledge on the given subject. The more dont-to-earth reason may be safety. If someone performs an experiment without knowledge of its true results it might result in some danger to the safety of those perforning it without knowledge of all the risks.

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3 years ago

A car changes speed from 25 m/s to 10 m/s in 240 seconds. Describe its acceleration.​

A car changes speed from 25 m/s to 10 m/s in 240 seconds. Describe its acceleration.