Answer:
the length of the simple pendulum is 0.25 m.
Explanation:
Given;
mass of the air-track glider, m = 0.25 kg
spring constant, k = 9.75 N/m
let the length of the simple pendulum = L
let the frequency of the air-track glider which is equal to frequency of simple pendulum = F
The oscillation frequency of air-track glider is calculated as;

The frequency of the simple pendulum is given as;

Thus, the length of the simple pendulum is 0.25 m.
The displacement vector (SI units) is
![\vec{r} =At\hat{i}+A[t^{3}-6t^{2}]\hat{j}](https://tex.z-dn.net/?f=%5Cvec%7Br%7D%20%3DAt%5Chat%7Bi%7D%2BA%5Bt%5E%7B3%7D-6t%5E%7B2%7D%5D%5Chat%7Bj%7D)
The speed is a scalar quantity. Its magnitude is

Answer: At√(t⁴ - 12t³ + 36t² + 1)
Answer:
1) Current decreases; 2) Inverse proportionally; 3) 1[A]
Explanation:
1)
As we can see as the resistance increases the current decreases, if we take two points as an example, when the resistance is equal to 50 [ohms] the current is equal to 1[amp] and when the resistance is equal to 200 [ohms] the current tends to have a value below 0.5 [amp]. Thus demonstrating the decrease in current.
2)
Inverse proportionally, by definition we know that the law of ohm determines the voltage according to resistance and amperage. This is the voltage will be equal to the product of the voltage by the resistance.
![V=I*R\\V = voltage [volts]\\I = current[amp]\\R = resistance [ohms]](https://tex.z-dn.net/?f=V%3DI%2AR%5C%5CV%20%3D%20voltage%20%5Bvolts%5D%5C%5CI%20%3D%20current%5Bamp%5D%5C%5CR%20%3D%20resistance%20%5Bohms%5D)
where:

And whenever we have in a fractional number the denominator the variable we are interested in, we can say that this is inversely proportional to the value we are interested in determining. In this case, we can see from the two previous expressions that both the current and the resistance appear in the denominator, therefore they are inversely proportional to each other.
3)
If we place ourselves on the graph on the resistance axis, we see that at 50 [ohm] will correspond a current value equal to 1 [A].
The relationship between the distance covered, initial and final speeds, and time can be expressed through the equation,
First equation,
2ad = Vf² - Vi²
Substituting the known values,
2(a)(0.230 km) = (70 km/h)² - (40 km/h)²
The value of a from the equation is 7173.92 km/h².
Second equation,
d = (Vi)(t) + 0.5at²
Substituting the known values,
0.230 km = (40 km/h)(t) + (0.5)(7173.92 km/h²)(t²)
The value of t from the equation is 4.1818 x 10^-3 hours which is also equal to 0.2509 minutes or 15 seconds.
Answer: 15 seconds