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**a**3. 0.5m[ (dx/dt)^2 + 2(dy/dt)^2 ] + 0.5k[y(t) - x(t) -**a**]^2 = 0.5m(**v**_0)^2 (**v**_0)^2 - (dx/dt)^2 - 2(dy/dt)^2 = (**k**/**m**)[y(t) - x(t) -**a**]^2 4. When dx/dt = 0 then dy/dt =**v**_0 / 2 Plug into energy d_1...1 Answers · Science & Mathematics · 28/06/2019

...1.50)

**v**^2 1/2 's cancel 3.5 = 0.56 + 1.50**v**^2 1.50 ^2 = 2.94**v**^2 = 1.96**v**= 1.4**m**/s When you get**a**good response, please consider giving**a**best answer. This is...1 Answers · Science & Mathematics · 17/04/2019

1) E = 1/2

**k****A**^2 E = 0.5 * 275 * 0.058^2 = 0.46 J 2)**v**= w**A**= sqrt(**k**/**m**)**A****v**= sqrt(275/0.582) * 0.058 = 1.26**m**/s 3)**a**= w^2**A**= (**k**/**m**)**A****a**= (275/0.582) * 0.058 = 27.41**m**/s^22 Answers · Science & Mathematics · 08/08/2019

...61.2 / 5) ω = 3.50 rad/s x = Acos(ωt + φ)

**v**= -ωΑsin(ωt + φ) 2 = -3.50Αsin(3...find the amplitude -0.33 = Acos(3.5(0) + 1.047)**A**= -0.660**m**Now we find the times when the position...1 Answers · Science & Mathematics · 29/04/2019

...solution using 0.100

**M**benzoic acid (p**K****a**= 4.20 ) and 0.160**M**sodium benzoate. pH = pKa + log...-]/[HA] = 10^-0.20 = 0.631**V**= vol. sodium benzoate 100.0-**V**= vol. benzoic...1 Answers · Science & Mathematics · 06/02/2020

... need to accelerate from 0

**m**/s to 82.1**m**/s in**a**space of 2000 meters**a**(t) =**a****v**(t) = int(**a*** dt) = at + C**v**(0) = 0**v**(t... s(0) = 0 s(t) = (1/2) ***a*** t^2**v**(**k**) = 82.1 s(**k**) = 2000 82.1 =**a*****k**2000 = (1/2...1 Answers · Science & Mathematics · 18/07/2019

...; solve for

**M****M**= mRT/(PV) ... note that density =**m**/**V****M**= dRT/P**M**= (8.51g/L)(8.314 L kPa/mole**K**)(325**K**) / (88.6 kPa)**M**= 259.53 g/mole <&...4 Answers · Science & Mathematics · 28/07/2019

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**a**) pi*(16 ft)*(3 ft)^2 = 144 pi ft^3. (b)**V**= pi*h*r^2 => dV/dt = pi*r^2 dh/dt or in this case 9*pi dh/dt. (c) dV/dt =**k***h^(1/2) =>**k**= (-2) / sqrt(16) = -1/2. 9*pi dh/dt = (-1/2)*h^(1/2) => 18*pi...2 Answers · Science & Mathematics · 11/08/2019

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**a**) easiest is v² = ... * 3.0m = 89 m²/s²**v**= 9.4**m**/s (b) KE + GPE become "spring... I'll assume you meant**k**= 5.2E4 N/**m**½...1 Answers · Science & Mathematics · 07/02/2020

... + GPE as leaves spring 1/2

**k**x^2 = 1/2**m****v**^2 +**m**g h 1/2(630)(0.18^2) = 1/2 (0.19)**v**^2 + 0.19...5) = 51.95 Vf = 7.2**m**/s When you get**a**good response, please consider giving**a**best...1 Answers · Science & Mathematics · 03/07/2019

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