Answer:
The required equation is y(t) = -10.34 + 0.4t + 10.4e^(-0.038t)
The velocity is the first derivative of y(t)
The acceleration is the second derivative of y(t).
Explanation:
The required equation is found by taking the first and second derivative for velocity and acceleration respectively and setting the equations given to the boundary conditions given. The complete solution can be found in the attachment below.
Thank you for reading.
Answer:
Look below.
Explanation:
If additives are having negative effects on health and the environment, it would be wise to not use detergents containing these additives. These additives could threaten living things such as humans and animals.
Answer:
I know 1, that is in the case of a burning of a candle.
Explanation:
Answer:
Time period of oscillations is 0.62 s
Explanation:
Due to suspension of weight the change in the length of the spring is given as
![\Delta L = L_f - L_i](https://tex.z-dn.net/?f=%5CDelta%20L%20%3D%20L_f%20-%20L_i)
![\Delta L = 21.5 - 11.9 = 9.6 cm](https://tex.z-dn.net/?f=%5CDelta%20L%20%3D%2021.5%20-%2011.9%20%3D%209.6%20cm)
now we know that spring is stretched due to its weight so at equilibrium the force due to weight is counter balanced by the spring force
![mg = kx](https://tex.z-dn.net/?f=mg%20%3D%20kx)
![0.037 (9.81) = k(0.096)](https://tex.z-dn.net/?f=0.037%20%289.81%29%20%3D%20k%280.096%29)
![k = 3.78 N/m](https://tex.z-dn.net/?f=k%20%3D%203.78%20N%2Fm)
Now the period of oscillation of spring is given as
![T = 2\pi \sqrt{\frac{m}{k}}](https://tex.z-dn.net/?f=T%20%3D%202%5Cpi%20%5Csqrt%7B%5Cfrac%7Bm%7D%7Bk%7D%7D)
Now plug in all values in it
![T = 2\pi \sqrt{\frac{0.037}{3.78}}](https://tex.z-dn.net/?f=T%20%3D%202%5Cpi%20%5Csqrt%7B%5Cfrac%7B0.037%7D%7B3.78%7D%7D)
![T = 0.62 s](https://tex.z-dn.net/?f=T%20%3D%200.62%20s)