Question

• always use significant figure rules. remember that these rules apply to all numbers that are measurements. you travel 20.0 mph for 0.500 hour, 40.0 mph for 1.00 hour, 30.0 mph for 0.500 hour, and 50.0 mph for 2.00 hours. what is the average speed?

○ 41.3 mph
○ 165 mph
○ 65 mph
○ 23.5 mph

Explanation:

Step1: Calculate total distance for each segment

For the first segment: \( \text{Distance}_1 = \text{Speed}_1 \times \text{Time}_1 = 20.0 \, \text{mph} \times 0.500 \, \text{hour} = 10.0 \, \text{miles} \)
For the second segment: \( \text{Distance}_2 = \text{Speed}_2 \times \text{Time}_2 = 40.0 \, \text{mph} \times 1.00 \, \text{hour} = 40.0 \, \text{miles} \)
For the third segment: \( \text{Distance}_3 = \text{Speed}_3 \times \text{Time}_3 = 30.0 \, \text{mph} \times 0.500 \, \text{hour} = 15.0 \, \text{miles} \)
For the fourth segment: \( \text{Distance}_4 = \text{Speed}_4 \times \text{Time}_4 = 50.0 \, \text{mph} \times 2.00 \, \text{hours} = 100.0 \, \text{miles} \)

Step2: Calculate total distance

\( \text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 + \text{Distance}_3 + \text{Distance}_4 = 10.0 + 40.0 + 15.0 + 100.0 = 165.0 \, \text{miles} \)

Step3: Calculate total time

\( \text{Total Time} = \text{Time}_1 + \text{Time}_2 + \text{Time}_3 + \text{Time}_4 = 0.500 + 1.00 + 0.500 + 2.00 = 4.00 \, \text{hours} \)

Step4: Calculate average speed

\( \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{165.0}{4.00} = 41.25 \, \text{mph} \approx 41.3 \, \text{mph} \) (using significant figure rules)

Answer:

41.3 mph