Balanced vs. Unbalanced Forces - Questions 9 Help

When the forces acting upon an object are balanced, the object will maintain its state of motion; that is, its velocity remains constant. If the forces are unbalanced, the object will either speed up or slow down. The reverse logic is also true: if an object has a constant velocity, then the forces are balanced. And if an object is speeding up or slowing down, the forces are unbalanced.

The slope of a velocity-time graph is the acceleration of the object. If the slope is zero - i.e., the line is horizontal - then the object has zero acceleration. In other words, the object is moving with a constant speed in an unchanging direction. In such a situation, the forces acting upon the object are balanced.

Alternatively, if the line has a slope, then the object is accelerating. As such, the forces are unbalanced. To determine if the acceleration is the speeding-up variety or the slowing-down variety, one must observe whether the line is approaching the v=0 m/s axis or progressing away from it. If the line approaches the time axis (v=0 m/s), then the object is slowing down. On the other hand, if the line is progressing away from time axis over the course of its motion, then the object is speeding up. Either case involves an unbalanced force.

Note that in the above discussion that it did not matter whether or not the line was in the positive region of the graph or in the negative region of the graph. What matters is whether or not the line is horizontal (for constant speed), approaching the time axis (for slowing down), or progressing away from it (for speeding up).