Question

comparing linear relationships
student 2
two bikers rode at a constant speed on a 150 - meter track. the data here show each bikers distance for a certain part of the race. who won the race and by how much?
student 1
won the race by about

Explanation:

Step1: Calculate the speed of Student 1

From the table, for Student 1, when \(t = 4\) sec, \(d=40\) m. Speed \(v=\frac{d}{t}\). So \(v_1=\frac{40}{4} = 10\) m/s. To cover \(d = 150\) m, using the formula \(t=\frac{d}{v}\), \(t_1=\frac{150}{10}=15\) sec.

Step2: Calculate the speed of Student 2

From the graph, using two points \((4,42)\) and \((6,63)\). Speed \(v=\frac{\Delta d}{\Delta t}\). \(\Delta d=63 - 42=21\) m, \(\Delta t=6 - 4 = 2\) sec. So \(v_2=\frac{21}{2}=10.5\) m/s. To cover \(d = 150\) m, using \(t=\frac{d}{v}\), \(t_2=\frac{150}{10.5}=\frac{1500}{105}=\frac{100}{7}\approx14.29\) sec.

Step3: Find the difference in time

\(\Delta t=t_1 - t_2=15-\frac{100}{7}=\frac{105 - 100}{7}=\frac{5}{7}\approx0.71\) sec.

Answer:

Student 2 won the race by about \(0.7\) seconds.