Answer: ![- 0.1250 cm/s^2](https://tex.z-dn.net/?f=%20-%200.1250%20cm%2Fs%5E2)
Acceleration is rate of change of velocity.
The equation of turtle's position as a function of time is given by:![x(t)=50+2t-0.0625t^2](https://tex.z-dn.net/?f=x%28t%29%3D50%2B2t-0.0625t%5E2)
Differentiate the above equation to find the velocity as a function of time:
![\frac{dx}{dt}=v(t)=2-2\times 0.0625t](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%3Dv%28t%29%3D2-2%5Ctimes%200.0625t)
Differentiating further, we would get the equation for acceleration:
![\frac{d^2x}{dt^2}=a(t)=-0.1250\\ \Rightarrow a(0)=-0.1250](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2x%7D%7Bdt%5E2%7D%3Da%28t%29%3D-0.1250%5C%5C%20%5CRightarrow%20a%280%29%3D-0.1250)
Therefore, initial acceleration is ![- 0.1250 cm/s^2](https://tex.z-dn.net/?f=%20-%200.1250%20cm%2Fs%5E2)
Answer:
The magnitude of the centripetal force to make the turn is 3,840 N.
Explanation:
Given;
radius of the cured road, r = 400 m
speed of the car, v = 32 m/s
mass of the car, m = 1500 kg
The magnitude of the centripetal force to make the turn is given as;
![F_c = \frac{mv^2}{r}](https://tex.z-dn.net/?f=F_c%20%3D%20%5Cfrac%7Bmv%5E2%7D%7Br%7D)
where;
Fc is the centripetal force
![F_c = \frac{mv^2}{r} \\\\F_c = \frac{(1500)(32)^2}{400}\\\\F_c = 3,840 \ N](https://tex.z-dn.net/?f=F_c%20%3D%20%5Cfrac%7Bmv%5E2%7D%7Br%7D%20%5C%5C%5C%5CF_c%20%3D%20%5Cfrac%7B%281500%29%2832%29%5E2%7D%7B400%7D%5C%5C%5C%5CF_c%20%3D%203%2C840%20%5C%20N)
Therefore, the magnitude of the centripetal force to make the turn is 3,840 N.
Given :
An object 50 cm high is placed 1 m in front of a converging lens whose focal length is 1.5 m.
To Find :
the image height (in cm).
Solution :
By lens formula :
![\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7Bv%7D%20-%20%5Cdfrac%7B1%7D%7Bu%7D%20%3D%20%5Cdfrac%7B1%7D%7Bf%7D)
Here, u = - 100 cm
f = 150 cm
![\dfrac{1}{v} - \dfrac{1}{-100} = \dfrac{1}{150}\\\\v = - 300 \ cm](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7Bv%7D%20-%20%5Cdfrac%7B1%7D%7B-100%7D%20%3D%20%5Cdfrac%7B1%7D%7B150%7D%5C%5C%5C%5Cv%20%3D%20-%20300%20%5C%20cm)
Now, magnification is given by :
![m = \dfrac{v}{u} = \dfrac{h_i}{h_o}\\\\h_i = \dfrac{300}{100}\times 1\\\\h_i = 3 \ m](https://tex.z-dn.net/?f=m%20%3D%20%5Cdfrac%7Bv%7D%7Bu%7D%20%3D%20%5Cdfrac%7Bh_i%7D%7Bh_o%7D%5C%5C%5C%5Ch_i%20%3D%20%5Cdfrac%7B300%7D%7B100%7D%5Ctimes%201%5C%5C%5C%5Ch_i%20%3D%203%20%5C%20m)
Therefore, the image height is 3 m or 300 cm.
Answer:
The potential between the plates will decrease.
Explanation:
An insulator is usually placed between the parallel plates and is also called a dielectric because it makes the amount of charge a capacitor can accommodate to increase at a particular potential difference.
Furthermore, the dielectric effect will make the electric field of the charged capacitor which is not connected to a source of supply to decrease.
Now, when the battery is removed, the charge Q remains constant and Capacity C will increase.
Formula for the potential difference is here;
V = Q/C
Since the numerator Q is constant and the denominator C increases, it means the potential difference V will decrease