Question

determining acceleration from a velocity - time graph
the graphs display velocity data. velocity is on the y - axis (m/s), while time is on the x - axis (s). based on the graphs, which data set represents constant acceleration?

Explanation:

Step1: Recall acceleration - velocity graph concept

Acceleration is the slope of the velocity - time graph. Constant acceleration means a constant slope.

Step2: Analyze first graph

The first graph has a straight - line. The slope between any two points is the same. For example, between (0,0) and (1,1), slope $m=\frac{1 - 0}{1 - 0}=1$. Between (2,2) and (3,3), slope $m=\frac{3 - 2}{3 - 2}=1$.

Step3: Analyze second graph

The second graph is a curve. The slope is changing at different points. For example, near the start the slope is small, and as we move to the right, the slope increases.

Step4: Analyze third graph

The third graph is a horizontal line. The slope is 0, which means zero acceleration (a special case of constant acceleration where the value of acceleration is 0). But we are looking for non - zero constant acceleration. The first graph has a non - zero constant slope.

Answer:

The first graph represents constant acceleration.