Alan

Subtract 5 from both sides to get -1 -5 = x/6  or  -6 = x/6

Multiply both sides by 6:  -6*6 = x  or  -36 = x   (we can also write this as x = -36)

Density is mass per unit volume, so for the copper we have

8.92*10^3= 100/V  so V = 100/(8.92*10^3)  = 1/89.2 L

For magnesium:   1.74*10^3 = M/(1/89.2)  so  M = 1.74*10^3/89.2 ≈ 19.51 g

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For anyone uncomfortable with the determination of the limiting values as δt goes to zero in the above, here are graphical representations of those limits:

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The following illustrates geno3141's answer.

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I made some errors in my previous analysis.  A more general approach is derived and used here:

So, in question 3.7 the result is a reduction in speed and in question 3.8 an increase in speed.

(I've used δa for acceleration, but should probably have just used a.  I had δv = aδt in mind .  This doesn't affect the analysis though.)

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In error - see below.

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For question 3.7:

Not quite right - see below.

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Not clear to me either.  The arrangement of the two objects isn't specified (Is one on top of the other?  If so, which is which?); what does the 2-4 represent (no units are given); where are the forces applied?

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I don't know.  He/she might want the total derivative in the form dF = f_xdx + f_ydy + f_zdz, but, if so, the reply in the other thread should help.

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Q3.3   For an object to be accelerating it must either be changing speed or direction or both.  The question states the object is moving at constant speed, so it can only be accelerating when it is changing direction.  At point C it is not changing direction, it is travelling in a straight line.  So, at C it is changing neither speed nor direction; therefore it is a point of zero acceleration.  At the other points its direction is changing, hence it is accelerating, hence they are not points of zero acceleration.

Q3.7 and 3.8 I'll do a more complete analysis with a diagram later.