- #1
schaefera
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Say you have know the fact that, as something moves along a horizontal surface, a retarding force F= -kv acts on it. Obviously you can use a differential equation to solve for velocity as a function of time; let's assume you get something like v(t)=5 e^(-kt/m). I know that this works out right.
But now, suppose you want to integrate velocity as a function of time to get position. You'd get something like x(t)= -5m/k e^(-kt/m). Why is there a negative sign in the position function? If the object is moving toward the positive direction, shouldn't the sign of position be positive, as it approaches some point at which is stops moving? What's going on with the negative from integration?
But now, suppose you want to integrate velocity as a function of time to get position. You'd get something like x(t)= -5m/k e^(-kt/m). Why is there a negative sign in the position function? If the object is moving toward the positive direction, shouldn't the sign of position be positive, as it approaches some point at which is stops moving? What's going on with the negative from integration?