Question

1. to the right is a position - time graph of a runner. first, sketch what you think his velocity - time graph will look like on the blank axes at the far right. then check your answer in the gizmo.

Explanation:

Step1: Recall velocity - time relationship

Velocity is the rate of change of position. For a linear position - time graph, the velocity is constant.

Step2: Calculate velocity from position - time graph

The position - time graph is a straight line. The initial position $x_1 = 2$ yards at $t_1=0$ seconds and the final position $x_2 = 40$ yards at $t_2 = 4$ seconds. The velocity $v=\frac{\Delta x}{\Delta t}=\frac{x_2 - x_1}{t_2 - t_1}=\frac{40 - 2}{4-0}=\frac{38}{4}=9.5$ yards per second.

Step3: Sketch velocity - time graph

Since the velocity is constant, the velocity - time graph will be a horizontal line at $v = 9.5$ yards per second.

Answer:

The velocity - time graph will be a horizontal line at $v = 9.5$ yards per second on the given velocity - time axes.