Question

which of the following graphs describes the movement of the fastest runner?

Explanation:

Step1: Recall speed - distance - time relation

Speed $v=\frac{\Delta d}{\Delta t}$, and on a distance - time graph, the slope represents speed.

Step2: Analyze Graph A

Starting at $d = 20$ m, in 4 seconds, it moves to $d = 40$ m. $\Delta d=40 - 20=20$ m, $\Delta t = 4$ s, $v_A=\frac{20}{4}=5$ m/s.

Step3: Analyze Graph B

Starts at $d = 0$ m, in 4 seconds, it moves to $d = 30$ m. $\Delta d=30 - 0 = 30$ m, $\Delta t=4$ s, $v_B=\frac{30}{4}=7.5$ m/s.

Step4: Analyze Graph C

Distance is constant ($d = 40$ m), so speed $v_C = 0$ m/s.

Step5: Analyze Graph D

Starting at $d = 20$ m, in 4 seconds, it moves to $d = 30$ m. $\Delta d=30 - 20 = 10$ m, $\Delta t=4$ s, $v_D=\frac{10}{4}=2.5$ m/s.

Answer:

b. Graph B