A car traveling at 24 m/s starts to decelerate steadily. It comes to a complete stop in 8 seconds. What is its acceleration?

1 answer:

6 0

Formula for velocity:
V(t) = Vi + at
Where V(t) is velocity at time t, Vi is initital velocity, and a is acceleration.
Solving for a:
V(8) = Vi + a(8)
V(8) = 0 (car has stopped)
0 = 24 + 8a
-24 = 8a
a = -3 m/s/s

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Lead atoms occupy a volume of 3 x 10-29 m3. Each atom contributes two free electrons. Calculate the Fermi velocity of lead.

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<u>Answer:</u> The Fermi velocity of lead is 64.4 km/s.

<u>Explanation:</u>

To calculate the Fermi velocity, we use the equation:

$V_f=\frac{h}{2\pi m_e}(\frac{3\pi^2N}{V})^{1/3}$

where,

h = Planck's constant = $6.62\times 10^{-34}Js$

$m_e$ = mass of electron = $9.1\times 10^{-31}kg$

N = Number of atoms present in per volume of atom multiplied by number of electrons present in given atom = $\frac{2\times N_A\times V}{M}$

$N_A$ = Avogadro's number = $6.022\times 10^{26}mol^{-1}$ (When the mass is in kilograms)

V = Volume = $3\times 10^{-29}m^3$

M = molecular weight of lead = 207.2 g/mol

Putting values in above equation, we get:

$V_f=\frac{6.62\times 10^{-34}}{2\times 3.14\times (9.1\times 10^{-31})}(\frac{3\times (3.14)^2\times (2\times 6.022\times 10^{23}\times 3\times 10^{-29})}{3\times 10^{-29}\times 207.2})^{1/3}$