Thursday, November 24, 2016

newtonian mechanics - Why is it that a force is not required for a body to move at constant velocity?


A body continues in its state of motion unless a force is applied to it. But how does an object stay in motion in the first place? A force must have caused it to move right?



Answer



While you know the statement of Newton's first law, Newton's second law can be used to answer your question. Newton's second law is stated mathematically as $$\vec{F} = m\vec{a}$$


This statement tells us that, for a given object of mass $m$, the acceleration of that object (whether it speeds up, slows down, or travels at a constant velocity), is directly proportional to the net force applied to it. Thus, if a net force is applied to an object initially at rest, the object will accelerate in the direction of the force (so yes, a force is required for an object to begin moving initially). However, if the force is then no longer applied to the object, then $\vec{a} = \frac{\vec{F}}{m} = \frac{0\text{N}}{m} = 0 \frac{\text{m}}{\text{s}^2}$. Thus, the object's speed will not change. So, in short, "staying in motion" (traveling at a constant velocity and following a straight line) is the "default" action of a given object. If the object was speeding up or slowing down, $\vec{F} \neq 0$.


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