Question

study the distance - time graph in the diagram. according to the graph, where does the object have the greatest speed? o 4 o 2 o 3 o 1

Explanation:

Step1: Recall speed - distance - time relation

Speed is the slope of a distance - time graph. Mathematically, $s=\frac{\Delta d}{\Delta t}$, where $s$ is speed, $\Delta d$ is change in distance and $\Delta t$ is change in time.

Step2: Analyze slope of each segment

• Segment 1: From $(0,0)$ to $(4,10)$. $\Delta d = 10 - 0=10$ meters, $\Delta t=4 - 0 = 4$ seconds. Slope $s_1=\frac{10}{4}=2.5$ m/s.
• Segment 2: From $(4,10)$ to $(8,25)$. $\Delta d = 25 - 10 = 15$ meters, $\Delta t=8 - 4=4$ seconds. Slope $s_2=\frac{15}{4}=3.75$ m/s.
• Segment 3: From $(8,25)$ to $(10,55)$. $\Delta d = 55 - 25 = 30$ meters, $\Delta t=10 - 8 = 2$ seconds. Slope $s_3=\frac{30}{2}=15$ m/s.
• Segment 4: From $(10,55)$ to $(14,60)$. $\Delta d = 60 - 55 = 5$ meters, $\Delta t=14 - 10 = 4$ seconds. Slope $s_4=\frac{5}{4}=1.25$ m/s.

Answer:

3