Final answer:
Jacob takes 60 seconds to catch up to Pablo, covering a distance of 180 meters. Jacob's final velocity is 6 m/s.
Step-by-step explanation:
To find the answer to each part of the question, we need to analyze the motion of the two runners. Let's start with part (a).
(a) To find how long it takes Jacob to catch Pablo, we can use the equation: (Velocity of Jacob - Velocity of Pablo) / Acceleration = Time. In this case, the velocity of Jacob is 3 m/s (same as Pablo) and the acceleration is 0.05 m/s². Substituting these values into the equation, we get: (3 m/s - 0 m/s) / 0.05 m/s² = 60 seconds.
(b) To find the distance covered by Jacob, we can use the equation: Distance = Initial Velocity × Time + (1/2) × Acceleration × Time². In this case, the initial velocity is 3 m/s (same as Pablo), the acceleration is 0.05 m/s², and the time is 60 seconds. Substituting these values into the equation, we get: Distance = 3 m/s × 60 seconds + (1/2) × 0.05 m/s² × (60 seconds)² = 180 meters.
(c) The final velocity of Jacob can be found using the equation: Final Velocity = Initial Velocity + Acceleration × Time. In this case, the initial velocity is 3 m/s (same as Pablo), the acceleration is 0.05 m/s², and the time is 60 seconds. Substituting these values into the equation, we get: Final Velocity = 3 m/s + 0.05 m/s² × 60 seconds = 6 m/s.