In your question explains that an accelerometer is a device that uses the extension spring to measure acceleration in terms of Earth's Gravitational accelerations. So if this device is extended just 0.43 centimeters the possible accelerations is letter B. 0.80 g
Answer: A = y/cos32
That is the amplitude A in terms of the displacement y.
Explanation: Since the displacement in the question In the question is the same in both direction, it is a Simple Harmonic Motion problem. In s.h.m the amplitude of displacement A is related to the displacement itself y by this simple equation
y = A* cos(theta)
So, A = y/cos(theta)
A = y/cos32.
If the magnitude of the displacement y is given, you just substitute in.
The heat transferred is -30J
When the gas undergoes compression, work is done on the gas and its internal energy increases.
According to the first law of thermodynamics, the increase in internal energyΔU is the sum of the heat given to the gas ΔQ and the amount of work done on the gas ΔW

The work done on the gas is 150 J due to compression and the internal energy of the gas increases by 120 J.
Therefore, the heat given to the gas is given by,

Thus, an amount of heat equal to 30 J flows out of the system.
Answer:
This is a conceptual problem so I will try my best to explain the impossible scenario. First of all the two dust particles ara virtually exempt from any external forces and at rest with respect to each other. This could theoretically happen even if it's difficult for that to happen. The problem is that each of the particles have an electric charge which are equal in magnitude and sign. Thus each particle should feel the presence of the other via a force. The forces felt by the particles are equal and opposite facing away from each other so both charges have a net acceleration according to Newton's second law because of the presence of a force in each particle:

Having seen Newton's second law it should be clear that the particles are actually moving away from each other and will not remain at rest with respect to each other. This is in contradiction with the last statement in the problem.
Force equals mass*distance
F = ma
Given m = 10 kg, F = 30 N
30 = 10a
30/10 = a
3 = a
The wagon's acceleration is 3 m/s^2