Question

two vehicles start out traveling side by side along a straight road. their position functions, shown in the following graph, are given by s = f(t) and s = g(t), where s is measured in meters and t is measured in seconds. which vehicle has traveled farther at t = 2 seconds? vehicle f vehicle g what is the approximate velocity of the f vehicle at t = 3 seconds? meters per second what is the approximate velocity of the g vehicle at t = 3 seconds? meters per second which vehicle is traveling faster at t = 4 seconds? vehicle f vehicle g

Explanation:

Step1: Determine position at $t = 2$

Look at the graph for $t=2$. The $y -$ value (position $s$) of $s = f(t)$ is approximately $5$ and of $s = g(t)$ is approximately $4$. Since $5>4$, vehicle $f$ has traveled farther at $t = 2$ seconds.

Step2: Approximate velocity of $f$ at $t = 3$

Velocity is the slope of the position - time graph. For $s = f(t)$ at $t = 3$, we consider a small interval around $t = 3$. Let's take the interval from $t = 2$ to $t = 4$. At $t = 2$, $s_f(2)\approx5$ and at $t = 4$, $s_f(4)\approx9$. The average velocity $v=\frac{s_f(4)-s_f(2)}{4 - 2}=\frac{9 - 5}{2}=2$ meters per second.

Step3: Approximate velocity of $g$ at $t = 3$

For $s = g(t)$ at $t = 3$, consider the interval from $t = 2$ to $t = 4$. At $t = 2$, $s_g(2)\approx4$ and at $t = 4$, $s_g(4)\approx8$. The average velocity $v=\frac{s_g(4)-s_g(2)}{4 - 2}=\frac{8 - 4}{2}=2$ meters per second.

Step4: Determine which is faster at $t = 4$

The slope of the graph represents the velocity. At $t = 4$, the slope of $s = f(t)$ is steeper than the slope of $s = g(t)$. So vehicle $f$ is traveling faster at $t = 4$ seconds.

Answer:

1. Vehicle f
2. 2
3. 2
4. Vehicle f