Answer:
The response to your inquiry is: 15 m/s²
Explanation:
Equation x = at³ - bt² + ct
a = 4.1 m/s³
b = 2.2 m/s²
c = 1.7 m/s
First we calculate x at t = 4.1 s
x = 4.1(4.1)³ - 2.2(4.1)² + 1.7(4.1)
x = 4.1(68.921) - 2.2(16.81) + 6.97
x = 282.58 - 36.98 + 6.98
x = 252.58 m
Now we calculate speed
v = x/t = 252.58/ 4.1 = 61.6 m/s
Finally
acceleration = v/t = 61.6/4.1 = 15 m/s²
Response:
The intensity of light 18 feet underwater is about 0.02%
Clarification:
Employing Lambert's law
Let dI / dt = kI, where k is a proportionality factor, I represents the intensity of incident light, and t indicates the thickness of the medium
Then dI / I = kdt
Taking logarithms,
ln(I) = kt + ln C
I = Ce^kt
At t=0, I=I(0) implies C=I(0)
I = I(0)e^kt
At t=3 & I=0.25I(0), we find 0.25=e^3k
Solving for k gives k = ln(0.25)/3
k = -1.386/3
k = -0.4621
I = I(0)e^(-0.4621t)
I(18) = I(0)e^(-0.4621*18)
I(18) = 0.00024413I(0)
The intensity of light 18 feet underwater is about 0.2%
The wavelength can be calculated as Planck's constant divided by the momentum of the ball.
This translates to:
lambda = h / p.............> equation I
Momentum is equal to mass times velocity............> equation II
By substituting equation II into equation I, we obtain:
lambda = h / mv
Here are the values provided:
lambda = 8.92 * 10^-34 m
Planck's constant = 6.625 * 10^-34
velocity = 40 m/sec
Substituting these values into the previous equation, we calculate the mass as follows:
8.92*10^-34 = (6.625*10^-34) / (40*m)
mass = 0.0185678 kg
Answer:
A) and B) are valid.
Explanation:
When an object remains at rest, it is indicative that no net force acts upon it.
The downward gravitational force from Earth must be counterbalanced by an upward force of equal magnitude in order to maintain rest.
This upward force is provided by the normal force, which adjusts to satisfy Newton’s 2nd Law and is always perpendicular to the surface supporting the object (in this instance, the ground).
At the molecular level, this normal force comes from the ground's bonded molecules acting like tiny springs, compressed by the object’s molecules, providing an upward restorative force.
Thus, statements A) and B) are true.
