A man running uniformly at  8 𝑚/𝑠  is  16 𝑚  behind a bus when it starts accelerating at  2 𝑚𝑠−2. Time taken by him to board the bus is

To solve this problem, we need to understand that the man and the bus are moving in the same direction. The man is running at a constant speed, while the bus is accelerating from rest.

Step 1: Identify the given information

• The man's speed (v1) = 8 m/s
• The bus's acceleration (a) = 2 m/s²
• The initial distance between the man and the bus (d) = 16 m

Step 2: Understand the problem We need to find the time it takes for the man to catch up to the bus. This happens when the man and the bus have covered the same distance.

Step 3: Set up the equations We know that the distance covered by an object is given by the equation d = vt + 0.5at², where:

• d is the distance
• v is the initial velocity
• t is the time
• a is the acceleration

For the man, the equation becomes d = v1t (since he is not accelerating, a = 0) For the bus, the equation becomes d = 0.5a*t² (since it starts from rest, v = 0)

Step 4: Solve the equations We set the two equations equal to each other and solve for t:

v1t = 0.5a*t² 8t = t² t = 8 seconds

So, the man will catch up to the bus after 8 seconds.