Question

1. some people disregard the 30 mi/h speed limit (15 m/s) and travel at 60 mi/h (30 m/s) on the road described in question 1.

a) use the spreadsheet or calculator to calculate stop and go zones at 60 mi/h. sketch the intersection marking both zones. explain the danger of driving at this speed.
b) how would a decrease in the speed limit to 20 mi/h (about 10 m/s) affect the stop and go zones in question 1? use the spreadsheet or calculator to calculate both, then sketch the intersection, marking both zones.

Explanation:

Step1: Determine relevant physics - motion formulas

We use equations of motion like $d = vt$ (where $d$ is distance, $v$ is velocity and $t$ is time) for constant - speed motion. For the STOP zone, we may also consider reaction time and braking distance.

Step2: Calculate STOP and GO zones for 60 mi/h (30 m/s)

Let's assume a typical reaction time $t_{r}=1\ s$. The distance traveled during reaction time $d_{r}=v\times t_{r}=30\times1 = 30\ m$. For braking distance $d_{b}$, if we assume a constant deceleration $a$. Using $v^{2}=2ad_{b}$, we need to know the deceleration value. Let's assume a typical value of $a = 5\ m/s^{2}$, then $d_{b}=\frac{v^{2}}{2a}=\frac{30^{2}}{2\times5}=90\ m$. So the STOP zone is $d_{r}+d_{b}=30 + 90=120\ m$. The GO zone is the remaining distance to safely pass the intersection. The danger of driving at this speed is that the STOP zone is large, and if a driver realizes they need to stop late, they may not be able to stop in time and enter the intersection when it's not safe, increasing the risk of accidents.

Step3: Calculate STOP and GO zones for 20 mi/h (10 m/s)

The distance traveled during reaction time $d_{r}=v\times t_{r}=10\times1 = 10\ m$. Using the same deceleration $a = 5\ m/s^{2}$, $d_{b}=\frac{v^{2}}{2a}=\frac{10^{2}}{2\times5}=10\ m$. So the STOP zone is $d_{r}+d_{b}=10 + 10=20\ m$. The GO zone is adjusted accordingly. Sketching the intersection with these zones helps visualize the safe and non - safe areas for stopping and going.

Answer:

a) STOP zone is approximately 120 m (calculated as above). Sketch the intersection with a 120 - m zone marked as the STOP zone starting from a relevant point near the intersection. The danger is the increased risk of not being able to stop in time.
b) STOP zone is approximately 20 m (calculated as above). Sketch the intersection with a 20 - m zone marked as the STOP zone starting from a relevant point near the intersection.