A will take 11.02 seconds or 75.65 seconds to catch up with B.
Explanation
Runner A is carrying the baton and has a speed of 2.60 m/s . So, [tex]v= 2.60[/tex]
When A is 25.0 m behind the starting line, runner B starts from rest and accelerates at 0.0600 m/s². So, [tex]d_{0}= 25.0[/tex] and [tex]f= 0.0600[/tex]
Suppose, A will catch up with B to pass the baton to B after [tex]t[/tex] seconds.
Formula need to use here : [tex]d= \frac{1}{2}ft^2 -vt+d_{0}[/tex]
When A will catch up with B , then [tex]d=0[/tex]
So, the equation will be .......
[tex]0=\frac{1}{2}(0.0600)t^2 -(2.60)t+25.0\\ \\ 0=0.03t^2 -2.6t+25[/tex]
Using quadratic formula, we will get.....
[tex]t= \frac{-(-2.6)+/-\sqrt{(-2.6)^2 -4(0.03)(25)}}{2(0.03)}\\ \\ t= \frac{2.6+/-\sqrt{6.76-3}}{0.06} \\ \\ t= \frac{2.6+/-1.939}{0.06}\\ \\ t= 75.65, 11.02[/tex]
So, A will take 11.02 seconds or 75.65 seconds to catch up with B.
