Question

1. for each position-time graph, calculate and plot speed on the speed-time graph to the right.

a. the bicycle trip through hilly country
(position vs. time and speed vs. time graphs here)
b. a walk in the park
(position vs. time and speed vs. time graphs here)
c. strolling up and down the supermarket aisles
(position vs. time and speed vs. time graphs here)

Explanation:

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Part a: Bicycle Trip

Step1: Calculate 0-1hr speed

Speed = $\frac{\Delta \text{Position}}{\Delta \text{Time}} = \frac{15 - 0}{1 - 0} = 15$ MPH

Step2: Calculate 1-1.5hr speed

Speed = $\frac{15 - 15}{1.5 - 1} = 0$ MPH

Step3: Calculate 1.5-3hr speed

Speed = $\frac{30 - 15}{3 - 1.5} = 10$ MPH

Step4: Calculate 3-6hr speed

Speed = $\frac{40 - 30}{6 - 3} = \frac{10}{3} \approx 3.33$ MPH

Speed-Time Plot Guide for a:

• 0 to 1 hour: Horizontal line at 15 MPH
• 1 to 1.5 hours: Horizontal line at 0 MPH
• 1.5 to 3 hours: Horizontal line at 10 MPH
• 3 to 6 hours: Horizontal line at ~3.33 MPH

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Part b: Walk in the Park

Step1: Calculate 0-5min speed

Speed = $\frac{150 - 0}{5 - 0} = 30$ meters/min

Step2: Calculate 5-10min speed

Speed = $\frac{150 - 150}{10 - 5} = 0$ meters/min

Step3: Calculate 10-25min speed

Speed = $\frac{800 - 150}{25 - 10} = \frac{650}{15} \approx 43.33$ meters/min

Step4: Calculate 25-35min speed

Speed = $\frac{800 - 800}{35 - 25} = 0$ meters/min

Step5: Calculate 35-60min speed

Speed = $\frac{0 - 800}{60 - 35} = -32$ (speed = 32 meters/min)

Speed-Time Plot Guide for b:

• 0 to 5 minutes: Horizontal line at 30 meters/min
• 5 to 10 minutes: Horizontal line at 0 meters/min
• 10 to 25 minutes: Horizontal line at ~43.33 meters/min
• 25 to 35 minutes: Horizontal line at 0 meters/min
• 35 to 60 minutes: Horizontal line at 32 meters/min

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Part c: Supermarket Stroll

Step1: Calculate 0-15min speed

Speed = $\frac{50 - 0}{15 - 0} = \frac{10}{3} \approx 3.33$ feet/min

Step2: Calculate 15-25min speed

Speed = $\frac{15 - 50}{25 - 15} = -3.5$ (speed = 3.5 feet/min)

Step3: Calculate 25-35min speed

Speed = $\frac{60 - 15}{35 - 25} = 4.5$ feet/min

Step4: Calculate 35-55min speed

Speed = $\frac{0 - 60}{55 - 35} = -3$ (speed = 3 feet/min)

Speed-Time Plot Guide for c:

• 0 to 15 minutes: Horizontal line at ~3.33 feet/min
• 15 to 25 minutes: Horizontal line at 3.5 feet/min
• 25 to 35 minutes: Horizontal line at 4.5 feet/min
• 35 to 55 minutes: Horizontal line at 3 feet/min

Answer:

a. Bicycle Trip Speed Values:

• 0-1 hr: 15 MPH, 1-1.5 hr: 0 MPH, 1.5-3 hr: 10 MPH, 3-6 hr: ~3.33 MPH

b. Park Walk Speed Values:

• 0-5 min: 30 m/min, 5-10 min: 0 m/min, 10-25 min: ~43.33 m/min, 25-35 min: 0 m/min, 35-60 min: 32 m/min

c. Supermarket Stroll Speed Values:

• 0-15 min: ~3.33 ft/min, 15-25 min: 3.5 ft/min, 25-35 min: 4.5 ft/min, 35-55 min: 3 ft/min

Plot each constant speed segment as a horizontal line on the corresponding speed-time graph for each part.