The correct option is D.
Lumen is used to quantify the amount of total light energy that a source is putting out in all direction, thus, it refers to luminous output of a light source. Initial lumen refers to the luminosity of a light when it was first turned on; the luminosity is highest at this point.
-2/5 = 11k - k
-2/5 = 10k
-2/5/10 = k
-2/5 * 10 = k
-2/50 = k
k = -1/25.
-1/25 - 2/5 = 11k is true.
Here, height is given which will be the distance for a freely falling object.
The velocity will be
![v=\text{ }\frac{h}{t}](https://tex.z-dn.net/?f=v%3D%5Ctext%7B%20%7D%5Cfrac%7Bh%7D%7Bt%7D)
and the acceleration will be
![a=\frac{v}{t}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bv%7D%7Bt%7D)
In this way, the formula works.
Answer:
The height reached is 20m, The time taken to reach 20m is 2 seconds
Explanation:
Observing the equations of motion we can see that the following equation will be most helpful for this question.
![v^{2} = u^{2} + 2as](https://tex.z-dn.net/?f=v%5E%7B2%7D%20%3D%20u%5E%7B2%7D%20%2B%202as)
We are given initial velocity, u
We know that the stone will stop at its maximum height, so final velocity, v
Acceleration, a
And we are looking for the displacement (height reached), s
Substitute the values we are given into the equation
![0^{2} = 20^{2} + 2(10)s](https://tex.z-dn.net/?f=0%5E%7B2%7D%20%3D%2020%5E%7B2%7D%20%2B%202%2810%29s)
Rearrange for s
![0^{2} -20^{2} =20s](https://tex.z-dn.net/?f=0%5E%7B2%7D%20-20%5E%7B2%7D%20%3D20s)
![-400=20s](https://tex.z-dn.net/?f=-400%3D20s)
![\frac{-400}{20} =s](https://tex.z-dn.net/?f=%5Cfrac%7B-400%7D%7B20%7D%20%3Ds)
s = -20 (The negative is just showing direction, it can be ignored for now)
The height reached is 20m
Use a different equation to find the time taken
![s = vt - \frac{1}{2} at^{2}](https://tex.z-dn.net/?f=s%20%3D%20vt%20-%20%5Cfrac%7B1%7D%7B2%7D%20at%5E%7B2%7D)
Substitute in the values we have
![-20=(0)t - \frac{1}{2} (10)t^{2}](https://tex.z-dn.net/?f=-20%3D%280%29t%20-%20%5Cfrac%7B1%7D%7B2%7D%20%2810%29t%5E%7B2%7D)
Rearrange for t
![-20 =0 -5 t^{2}](https://tex.z-dn.net/?f=-20%20%3D0%20-5%20t%5E%7B2%7D)
![\frac{-20}{-5} =t^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-20%7D%7B-5%7D%20%3Dt%5E%7B2%7D)
![4 = t^{2}](https://tex.z-dn.net/?f=4%20%3D%20t%5E%7B2%7D)
t = 2s
The time taken to reach 20m is 2 seconds