To find the man's instantaneous velocity after 25 seconds, we need to use the equation of motion for uniformly accelerated motion:
v = u + at
Where: v = final velocity u = initial velocity a = acceleration t = time
Given that the man starts from rest (u = 0) and moves with uniform acceleration, we can rearrange the equation to solve for the final velocity:
v = u + at v = 0 + at v = at
We also know that the average velocity during the first 20 seconds is 2 m/s. The average velocity can be calculated using the formula:
Average velocity = (initial velocity + final velocity) / 2
Since the man starts from rest, the initial velocity is 0. We can substitute the values into the formula and solve for the acceleration:
2 m/s = (0 + v) / 2 4 m/s = v
Therefore, the final velocity after 20 seconds is 4 m/s. Now, we can find the acceleration using the formula:
v = at 4 m/s = a * 20 s
Solving for a:
a = 4 m/s / 20 s a = 0.2 m/s²
Now, we can find the instantaneous velocity after 25 seconds using the equation:
v = u + at v = 0 + (0.2 m/s²) * 25 s v = 5 m/s
Therefore, the man's instantaneous velocity after 25 seconds from his starting point is 5 m/s.