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3 years ago

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(a) a light-rail commuter train accelerates at a rate of 1.15 m/s2. how long does it take it to reach its top speed of 80.0 km/h

starting from rest?

1 answer:

snow_lady [41]3 years ago

6 0

A = 1.15m/s2, Vf = 80.0km/h --> we need it in m/s, so:
Vf = 80km/h × 1000m/1km × 1h/3600s
= 22.22m/s
Top speed = Vf, initial speed = Vi
time (t) = V(Vf-Vi) ÷ a
t = (22.22-0)m/s ÷ 1.15m/s2
t = 22.22m/s × s2/1.15m
= 19.32 seconds

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Total weight in tons

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Answer:

The half-life is $t_{1/2} = 1.005 h$

Explanation:

Using the decay equation we have:

$A=A_{0}e^{-\lambda t}$

Where:

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A(0) the initial activity
A is the activity at time t

We know the activity decrease by a factor of two in a one hour period (t = 1 h), it means that $A = \frac{A_{0}}{2}$

$\frac{A_{0}}{2}=A_{0}e^{-\lambda*1 h}$

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Taking the natural logarithm on each side we have:

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Now, the relationship between the decay constant λ and the half-life t(1/2) is:

$\lambda = \frac{ln(2)}{t_{1/2}}$

$t_{1/2} = \frac{ln(2)}{\lambda}$

$t_{1/2} = \frac{ln(2)}{0.69}$

$t_{1/2} = 1.005 h$

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2 years ago

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2 years ago

An ideal gas initially is allowed to expand isothermally until its volume of 1.6 L and pressure is 5 kPa, undergoes isothermal e

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(a) The work done by the gas during the isothermal expansion is -25.6 J.

(b) The heat added to the gas during this process is 25.6 J.

<h3>Net work done by the ideal gas against the external pressure</h3>

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The heat added to the gas is calculated as follows;

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1 year ago

A solenoidal coil with 22 turns of wire is wound tightly around another coil with 330 turns. The inner solenoid is 21.0 cm long

Airida [17]

Answer:

$0.00027646\ T$

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Mutual inductance is given by

$M=\dfrac{N_1\phi}{I}\\\Rightarrow M=\dfrac{22\times 1.14862\times 10^{-7}}{0.14}\\\Rightarrow M=2.33\times 10^{-5}\ H$

The mutual inductance of the two solenoids is $2.33\times 10^{-5}\ H$

Induced emf is given by

$\epsilon=-M\dfrac{dI_2}{dt}\\\Rightarrow \epsilon=-2.33\times 10^{-5}\times 1800\\\Rightarrow \epsilon=-0.04194\ V$

The emf induced in the outer solenoid by the changing current inthe inner solenoid is -0.04194 V

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