@ Jane. Sorry, perhaps I didn't quite get what you meant. But, I'll just try to explain the question from my perspective. Though, I think the answers and the question are implying what Paul just said (i.e. D>=0 is implied and hence heffernan's solutions apply).
Nonetheless, in my opinion, the question is ambiguous and can be taken in many ways.
If you took the friction to be the positive end, then sure D would be negative, but it wouldn't be both. Let's say the force is applied in the positive direction, then it would be 4.9 before it begins to move. However, stating that D goes in the negative direction then you are still saying that you are applying a negative force. If you were going to be REALLY picky, then you'd probably have to say D E (-4.9,0) OR D E (0,4.9) for your answer to make sense.
Think about it this way. The question states that a force is applied, but it doesn't state a direction. Now, if we look at that object. Given that one particular direction is taken as positive, can we state a specific direction in which this force has been applied? Of course we can't. Hence, the force can take both positive and negative values. Yes, you can technically apply a negative force. All forces are technically "applied." It will just be in the direction opposite to which is considered positive.
However, I think Paul's statement about magnitudes is probably what the question was asking. Luckily, VCAA doesn't make such vague questions/answers.
If you were going to be REALLY picky, then you'd probably have to say D E (-4.9,0) OR D E (0,4.9) for your answer to make sense.
Haha. If we stated D E (-4.9,0) OR D E (0,4.9). Remember that the term "or" implies the union symbol. Hence, D E (-4.9,0) OR D E (0,4.9) is the same as D E (-4.9,0) U (0,4.9) which is again, the same as D E (-4.9,4.9)\{0}. So, you essentially just said the same thing as me
But then again, I think the question implies that D is in the "positive" direction, as friction on a stationary surface with one mass is always against the direction of movement, and it is illogical to think that the friction force would ever be greater than the applied force... thus, the force will move in the D direction or not at all, making it silly to have D as the "negative" direction...
I know what you mean here and it would be illogical to even set the D direction as negative. But, mathematically speaking, it is possible. Thus, negative values of D should be considered. But, as you said, the question is implying magnitude (i.e. D is considered positive).
^ That probably doesn't make much sense haha but it just seems contradictory to say that D is in both the positive and negative direction at the same time, which is what you are saying with D E (-4.9,4.9)\{0}.
I don't quite get what you meant here. If we have the equation, Area = x^2. That x can only take a single value at any one time. The same applies to D in this situation. The D value would either be positive or negative. Sorry if I confused you earlier, but that was never the point I was making.
Hope I clarified anything. Then again, I could be wrong and apologies, in advance, if I am.
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