A runner of mass 57.5 kg starts from rest and accelerates with a constant acceleration of \(1.25 \mathrm{~m} / \mathrm{s}^{2}\) until she reaches a velocity of \(6.3 \mathrm{~m} / \mathrm{s}\). She then continues running with this constant velocity. a) How far has she run after 59.7 s? b) What is the velocity of the runner at this point?

Step 1: Finding the time taken to reach a constant velocity of 6.3 m/s We can use the equation \(v = u + at\) : Where \(v\) is the final velocity, \(u\) is the initial velocity, \(a\) is the acceleration, and \(t\) is the time. Given, \(v = 6.3 m/s\), \(u = 0 m/s\), and \(a = 1.25 m/s^2\). Using these values, we can find \(t\): \(6.3 = 0 + 1.25t\) Solving for \(t\), we get: \(t = 5.04s\) Step 2: Finding the distance covered during acceleration We can use the equation \(s = ut + \frac{1}{2}at^2\) : Where \(s\) is the distance, \(u\) is the initial velocity, \(a\) is the acceleration, and \(t\) is the time. Given, \(u = 0 m/s\), \(a = 1.25 m/s^2\), and \(t = 5.04 s\). Using these values, we can find \(s\) during acceleration: \(s = 0(5.04) + \frac{1}{2}(1.25)(5.04)^2\) Solving for \(s\), we get: \(s = 16.0 m\) Step 3: Finding the distance covered while running at a constant speed The total time was 59.7 s, and it took the runner 5.04 s to reach a constant speed of 6.3 m/s. Therefore, the time running at constant speed is \(59.7 - 5.04 = 54.66 s\). Now we use the equation \(s = vt\), we get: \(s = (6.3)(54.66)\) Solving for \(s\), we get: \(s = 344.3 m\) Step 4: Finding the total distance covered The total distance covered is the sum of the distance during acceleration and the distance while running at a constant speed, thus: Total distance = \(16.0 m + 344.3 m = 360.3 m\)

Since it took the runner 5.04 seconds to reach a constant.velocity of 6.3 m/s and the total.time of the.runner was 59.7 seconds, she has been.running at a constant 6.3 m/s.for we 54.66 seconds. As she is running at a constant speed, there is no additional.step needed: Velocity = 6.3 m/s