two vehicles start out traveling side by side along a straight road. their position functions, shown in the…

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

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

Answer

Explanation:

Step1: Check positions at t = 2

At t = 2, from the graph, the position of vehicle f, $s = f(2)$ is approximately 5 meters and the position of vehicle g, $s = g(2)$ is approximately 6 meters. Since $g(2)>f(2)$, vehicle g has traveled farther at t = 2 seconds.

Step2: Estimate velocity of f at t = 3

The velocity of a vehicle is the slope of the position - time graph. For vehicle f at t = 3, we can consider two points on the curve of $s = f(t)$ close to t = 3. Let's take (2,5) and (4,9). The slope $m=\frac{\Delta s}{\Delta t}=\frac{9 - 5}{4 - 2}=\frac{4}{2}=2$ meters per second. So the approximate velocity of the f vehicle at t = 3 seconds is 2 meters per second.

Step3: Estimate velocity of g at t = 3

For vehicle g at t = 3, consider two points on the line $s = g(t)$. Let's take (2,6) and (4,10). The slope $m=\frac{\Delta s}{\Delta t}=\frac{10 - 6}{4 - 2}=\frac{4}{2}=2$ meters per second. So the approximate velocity of the g vehicle at t = 3 seconds is 2 meters per second.

Step4: Compare velocities at t = 4

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

Answer:

Vehicle g 2 2 Vehicle f