Question

1. what kind of information is best displayed in an acceleration vs. time graph? whether an object is speeding up or slowing down an objects direction of motion an objects rate of motion the change in an objects velocity

Explanation:

• Whether an object is speeding up or slowing down: This depends on the relationship between velocity and acceleration, not directly shown on an acceleration - time graph.
• An object's direction of motion: Determined by the sign of velocity, not shown on an acceleration - time graph.
• An object's rate of motion: Rate of motion is velocity, not shown on an acceleration - time graph.
• The change in an object's velocity: Acceleration \(a=\frac{\Delta v}{\Delta t}\), so \(\Delta v=a\Delta t\). On an acceleration - time (\(a - t\)) graph, the area under the curve gives the change in velocity (\(\Delta v\)) as \(\Delta v=\int_{t_1}^{t_2}a\mathrm{d}t\) (for non - constant acceleration, it's the integral; for constant acceleration \(a\), \(\Delta v = a(t_2 - t_1)\) which is the area of the rectangle under the \(a - t\) graph).

Answer:

the change in an object's velocity