To find the final velocity attained by a body starting from rest and traveling a certain distance, we can use the equations of motion. In this case, we are given that the initial velocity (u) is 0 m/s, the time (t) is 30 seconds, and the distance (s) is 40 meters.
The equation that relates these variables is:
s = ut + (1/2)at^2
Since the initial velocity (u) is 0 m/s, the equation simplifies to:
s = (1/2)at^2
Rearranging the equation to solve for acceleration (a):
a = 2s / t^2
Plugging in the given values:
a = 2 * 40 / (30^2) = 80 / 900 = 0.0889 m/s^2
Now, to find the final velocity (v), we can use another equation of motion:
v = u + at
Since the initial velocity (u) is 0 m/s, the equation simplifies to:
v = at
Plugging in the calculated acceleration (a) and the given time (t):
v = 0.0889 * 30 = 2.67 m/s
Therefore, the final velocity attained after covering a distance of 40 meters in 30 seconds is 2.67 m/s.