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3241004551 [841]
3 years ago
10

Tim and Rick both can run at speed vr and walk at speed vw, with vr>vw. They set off together on a journey of distance D. Ric

k walks half of the distance and runs the other half. Tim walks half of the time and runs the other half.
1. How long does it take Rick to cover the distance D?
2. Find Rick's average speed for covering the distance D.
3. How long does it take Tim to cover the distance?
4. Who covers the distance D more quickly?
5. In terms of given quantities, by what amount of time, Delta t, does Tim beat Rick?
Physics
1 answer:
g100num [7]3 years ago
3 0

Answer:

Explanation:

1

t = D/2(vw) + D/2(vr)

2

V(ave) = 2.v(r).v(w) / [v(r) + v(w)]

3

t(T) = 2D / [v(w) + v(r)]

4

Tim does

5

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A series circuit has a capacitor of 0.25 × 10−6 F, a resistor of 5 × 103 Ω, and an inductor of 1 H. The initial charge on the ca
svetoff [14.1K]

Answer:

q=10^{-6}(e^{-4000t}-4e^{-1000t}+3)C

Explanation:

Given that L=1H, R=5000\Omega, \ C=0.25\times10^{-6}F, \ \ E(t)=12V, we use Kirchhoff's 2nd Law to determine the sum of voltage drop as:

E(t)=\sum{Voltage \ Drop}\\\\L\frac{d^2q}{dt^2}+R\frac{dq}{dt}+\frac{1}{C}q=E(t)\\\\\\\frac{d^2q}{dt^2}+5000\frac{dq}{dt}+\frac{1}{0.25\times10^{-6}}q=12\\\\\frac{d^2q}{dt^2}+5000\frac{dq}{dt}+4000000q=12\\\\m^2+5000m+4000000=0\\\\(m+4000)(m+1000)=0\\\\m=-4000  \ or \ m=-1000\\\\q_c=c_1e^{-4000t}+c_2e^{-1000t}

#To find the particular solution:

Q(t)=A,\ Q\prime(t)=0,Q\prime \prime(t)=0\\\\0+0+4000000A=12\\\\A=3\times10^{-6}\\\\Q(t)=3\times10^{-6},\\\\q=q_c+Q(t)\\\\q=c_1e^{-4000t}+c_2e^{-1000t}+3\times10^{-6}\\\\q\prime=-4000c_1e^{-4000t}-1000c_2e^{-1000t}\\q\prime(0)=0\\\\-4000c_1-1000c_2=0\\c_1+c_2+3\times10^{-6}=0\\\\#solving \ simultaneously\\\\c_1=10^{-6},c_2=-4\times10^{-6}\\\\q=10^{-6}e^{-4000t}-4\times10^{-6}e^{-1000t}+3\times10^{-6}\\\\q=10^{-6}(e^{-4000t}-4e^{-1000t}+3)C

Hence the charge at any time, t is q=10^{-6}(e^{-4000t}-4e^{-1000t}+3)C

6 0
3 years ago
Suppose you exert a 25-N force to lift a ball 0.4 m in 2 s. How much work is done?
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Examine the cross-sectional slice of a stem of a mint plant. Which statement most specifically describes mint?
Maslowich

The available options are:

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Answer:

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Explanation:

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