Question

graph velocity b (v_b) vs time a to b (t_ab) on the back side of this paper. make a graph of velocity versus time. velocity should be on the vertical axis (v_b). time should be on the horizontal axis (t_ab). analyze: what shape does the velocity versus time graph have? describe the line or curve that you get. what does the slope mean? v_a = \frac{1.9 cm}{t_a}, v_b = \frac{1.9 cm}{t_b}, a_{ab}=\frac{v_b - v_a}{t_{ab}}. show the calculations for one set of data above.

Explanation:

Step1: Recall velocity - time graph concept

In a velocity - time graph, the horizontal axis represents time ($t$) and the vertical axis represents velocity ($v$).

Step2: Analyze the slope of velocity - time graph

The slope of a velocity - time graph is given by the formula $\text{slope}=\frac{\Delta v}{\Delta t}$. The slope of a velocity - time graph represents acceleration. If the slope is zero, the velocity is constant (no acceleration). If the slope is positive, the object is accelerating (speeding up), and if the slope is negative, the object is decelerating (slowing down).

Step3: Determine the shape of the graph

Without specific data values for $v_A$, $v_B$ and $t_{AB}$, we can't make a numerical graph. But generally, if the acceleration is constant, the velocity - time graph is a straight - line. If the acceleration is changing, the graph is a curve.

Answer:

The horizontal axis of the velocity - time graph is time ($t_{AB}$) and the vertical axis is velocity ($v$). The slope of the velocity - time graph represents acceleration. The shape of the velocity - time graph can be a straight line if the acceleration is constant or a curve if the acceleration is changing.