Question

in a relay race, four runners (a, b, c, and d) work together to run a total distance of 400 m. each runner runs 100 m before handing a baton to the next runner. a clock starts measuring time when runner a begins. the time is recorded when each runner completes their part of the race. these times are shown on the distance vs. time graph below. which runner had the slowest average speed? choose 1 answer: a a b b c c d d

Explanation:

Step1: Recall average speed formula

Average speed is calculated as \( v = \frac{d}{t} \), where \( d \) is the distance traveled and \( t \) is the time taken. Each runner runs \( d = 100 \, \text{m} \), so we need to find the time each runner took to run 100 m and then compare their speeds (since distance is the same, the runner with the longest time will have the slowest speed).

Step2: Determine time for each runner

• Runner A: Starts at \( t = 0 \, \text{s} \) and ends at \( t = 20 \, \text{s} \). Time taken, \( t_A = 20 - 0 = 20 \, \text{s} \).
• Runner B: Starts at \( t = 20 \, \text{s} \) and ends at \( t = 60 \, \text{s} \). Time taken, \( t_B = 60 - 20 = 40 \, \text{s} \).
• Runner C: Starts at \( t = 60 \, \text{s} \) and ends at \( t = 80 \, \text{s} \). Time taken, \( t_C = 80 - 60 = 20 \, \text{s} \).
• Runner D: Starts at \( t = 80 \, \text{s} \) and ends at \( t = 100 \, \text{s} \). Time taken, \( t_D = 100 - 80 = 20 \, \text{s} \).

Step3: Compare times

We have \( t_A = 20 \, \text{s} \), \( t_B = 40 \, \text{s} \), \( t_C = 20 \, \text{s} \), \( t_D = 20 \, \text{s} \). Since \( t_B = 40 \, \text{s} \) is the longest time among them, and distance is the same (100 m) for all, runner B has the slowest average speed (because \( v \propto \frac{1}{t} \) when \( d \) is constant).

Answer:

B. B