Final answer:
The speed of the man is approximately 2.85 m/s and the acceleration of the bus is 0.11 m/s². The man can get approximately 152.25 meters close to the bus.
Step-by-step explanation:
To determine the speed of the man and the acceleration of the bus, we can use the equations of motion. Let's assume that the bus's acceleration is 'a' and the man's speed is 's'.
From the given information, we know that the bus travels 50m in 30s, so we can use the equation, s = ut + (1/2)at^2 to find the acceleration of the bus. Plugging in the values, we get 50 = 0 + (1/2)a(30)^2. Solving for 'a', we find that the bus has an acceleration of 0.11 m/s².
Now, since the man's speed is given as 3 m/s, we can find the time it takes for him to catch the bus by dividing the distance traveled by the relative velocity, which is the difference in their speeds. So, 30 = 50 / (3 - s). Solving for 's', we find that the man's speed is approximately 2.85 m/s.
Finally, to find out how close the man can get to the bus, we can use the equation of motion, s = ut + (1/2)at^2 for the man. Plugging in the values, we get d = 0 + 2.85(30) + (1/2)(0.11)(30)^2. Solving for 'd', we find that the man can get approximately 152.25 meters close to the bus.