Answer:
4 A
Explanation:
The relationship between current, voltage and resistance in a circuit is given by Ohm's law:

where
V is the voltage
R is the resistance
I is the current
The equation can also be rewritten as

from which we see that the current is inversely proportional to the resistance, R.
In this problem, the initial current is I = 8 A. Then the resistance is doubled:
R ' = 2R
So the new current is

so the current is halved.
To solve this problem we will apply the concepts related to energy conservation. From this conservation we will find the magnitude of the amplitude. Later for the second part, we will need to find the period, from which it will be possible to obtain the speed of the body.
A) Conservation of Energy,


Here,
m = Mass
v = Velocity
k = Spring constant
A = Amplitude
Rearranging to find the Amplitude we have,

Replacing,


(B) For this part we will begin by applying the concept of Period, this in order to find the speed defined in the mass-spring systems.
The Period is defined as

Replacing,


Now the velocity is described as,


We have all the values, then replacing,


Because the waves in the water with the fan like system.
Answer:
a = 0.7267
, acceleration is positive therefore the speed is increasing
Explanation:
The definition of acceleration is
a = dv / dt
they give us the function of speed
v = - (t-1) sin (t² / 2)
a = - sin (t²/2) - (t-1) cos (t²/2) 2t / 2
a = - sin (t²/2) - t (t-1) cos (t²/2)
the acceleration for t = 4 s
a = - sin (4²/2) - 4 (4-1) cos (4²/2)
a = -sin 8 - 12 cos 8
remember that the angles are in radians
a = 0.7267
the problem does not indicate the units, but to be correct they must be m/s²
We see that the acceleration is positive therefore the speed is increasing