Question

the motion of a leftward - moving object is represented by a position - time graph. (consider the positive direction to be to the right.)
is this a speeding up, slowing down, or constant speed motion?
speeding up slowing down constant speed
is the object experiencing balanced or unbalanced forces?
balanced unbalanced

Explanation:

Step1: Analyze the slope of the position - time graph

The slope of a position - time graph gives the velocity. The formula for the slope \(m=\frac{\Delta x}{\Delta t}\). For a leftward - moving object (negative direction), the slope is negative. As the graph is a curve, the slope is changing. The magnitude of the slope (since slope \(m = v\)) is decreasing. A decreasing magnitude of velocity (in the negative direction) means the object is slowing down.

Step2: Relate motion to forces

According to Newton's first law, an object has constant velocity (zero acceleration) when balanced forces act on it. When the velocity is changing (in this case, the magnitude of velocity is changing as the object is slowing down), there is an acceleration. From \(F = ma\) (Newton's second law), if \(a
eq0\), then \(F
eq0\). So, unbalanced forces act on the object.

Answer:

Slowing Down, Unbalanced