Given acceleration a = 5-3t, and its velocity is 7 at time t = 2, the value of s2 - s1 = 7
<h3>How to solve for the value of s2 - s1</h3>
We have
= ![\frac{dv}{dt} =v't = 5-3t\\\\\int\limits^a_b {v'(t)} \, dt](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3Dv%27t%20%3D%205-3t%5C%5C%5C%5C%5Cint%5Climits%5Ea_b%20%7Bv%27%28t%29%7D%20%5C%2C%20dt)
![= \int\limits^a_b {(5-3t)} \, dt](https://tex.z-dn.net/?f=%3D%20%5Cint%5Climits%5Ea_b%20%7B%285-3t%29%7D%20%5C%2C%20dt)
![5t - \frac{3t^2}{2} +c](https://tex.z-dn.net/?f=5t%20-%20%5Cfrac%7B3t%5E2%7D%7B2%7D%20%2Bc)
v2 = 5x2 - 3x2 + c
= 10-6+c
= 4+c
![s(t) = \frac{5t^2}{2} -\frac{t^3}{2} +3t + c](https://tex.z-dn.net/?f=s%28t%29%20%3D%20%5Cfrac%7B5t%5E2%7D%7B2%7D%20-%5Cfrac%7Bt%5E3%7D%7B2%7D%20%2B3t%20%2B%20c)
S2 - S1
![=(5*\frac{4}{2} -\frac{8}{2} +3*2*c)-(\frac{5}{2} *1^2-\frac{1^2}{2} +3*1*c)](https://tex.z-dn.net/?f=%3D%285%2A%5Cfrac%7B4%7D%7B2%7D%20-%5Cfrac%7B8%7D%7B2%7D%20%2B3%2A2%2Ac%29-%28%5Cfrac%7B5%7D%7B2%7D%20%2A1%5E2-%5Cfrac%7B1%5E2%7D%7B2%7D%20%2B3%2A1%2Ac%29)
= 6 + 6+c - 2+3+c
12+c-5+c = 0
7 = c
Read more on acceleration here: brainly.com/question/605631
Answer:
The principal stresses are σp1 = 27 ksi, σp2 = -37 ksi and the shear stress is zero
Explanation:
The expression for the maximum shear stress is given:
![\tau _{M} =\sqrt{(\frac{\sigma _{x}^{2}-\sigma _{y}^{2} }{2})^{2}+\tau _{xy}^{2} }](https://tex.z-dn.net/?f=%5Ctau%20_%7BM%7D%20%3D%5Csqrt%7B%28%5Cfrac%7B%5Csigma%20_%7Bx%7D%5E%7B2%7D-%5Csigma%20_%7By%7D%5E%7B2%7D%20%20%7D%7B2%7D%29%5E%7B2%7D%2B%5Ctau%20_%7Bxy%7D%5E%7B2%7D%20%20%20%20%7D)
Where
σx = stress in vertical plane = 20 ksi
σy = stress in horizontal plane = -30 ksi
τM = 32 ksi
Replacing:
![32=\sqrt{(\frac{20-(-30)}{2} )^{2} +\tau _{xy}^{2} }](https://tex.z-dn.net/?f=32%3D%5Csqrt%7B%28%5Cfrac%7B20-%28-30%29%7D%7B2%7D%20%29%5E%7B2%7D%20%2B%5Ctau%20_%7Bxy%7D%5E%7B2%7D%20%20%7D)
Solving for τxy:
τxy = ±19.98 ksi
The principal stress is:
![\sigma _{x}+\sigma _{y} =\sigma _{p1}+\sigma _{p2}](https://tex.z-dn.net/?f=%5Csigma%20_%7Bx%7D%2B%5Csigma%20_%7By%7D%20%3D%5Csigma%20_%7Bp1%7D%2B%5Csigma%20_%7Bp2%7D)
Where
σp1 = 20 ksi
σp2 = -30 ksi
(equation 1)
equation 2
Solving both equations:
σp1 = 27 ksi
σp2 = -37 ksi
The shear stress on the vertical plane is zero
Answer:
809.98°C
Explanation:
STEP ONE: The first step to take in order to solve this particular Question or problem is to find or determine the Biot value.
Biot value = (heat transfer coefficient × length) ÷ thermal conductivity.
Biot value = (220 × 0.1)÷ 110 = 0.2.
Biot value = 0.2.
STEP TWO: Determine the Fourier number. Since the Biot value is greater than 0.1. Tis can be done by making use of the formula below;
Fourier number = thermal diffusivity × time ÷ (length)^2.
Fourier number = (3 × 60 × 33.9 × 10^-6)/( 0.1)^2 = 0.6102.
STEP THREE: This is the last step for the question, here we will be calculating the temperature of the center plane of the brass plate after 3 minutes.
Thus, the temperature of the center plane of the brass plane after 3 minutes = (1.00705) (0.89199) (900- 15) + 15.
= > the temperature of the center plane of the brass plane after 3 minutes = 809.98°C.