a body travels from rest with acceleration 8ms find its velocity when it has covered a distance of 100m
x = (1/2) a t^2
200 = 8 t^2
t = 5 seconds
v = a t = 8 * 5 = 40 meters/ second
40
To find the velocity of the body when it has covered a distance of 100 meters, we can use the first equation of motion, which relates velocity (v), initial velocity (u), acceleration (a), and displacement (s):
s = ut + (1/2)at^2
Since the body starts from rest, its initial velocity (u) is 0. Thus, the equation becomes:
s = (1/2)at^2
Rearranging the equation, we get:
t^2 = 2s/a
Taking the square root of both sides, we can find the time (t) taken to cover a distance of 100 meters:
t = √(2s/a)
t = √(2 * 100 / 8)
t = √25
t = 5 seconds
Now that we know the time it took, we can find the final velocity (v) using the second equation of motion:
v = u + at
Since the initial velocity (u) is 0, the equation becomes:
v = at
v = 8 * 5
v = 40 m/s
Therefore, the velocity of the body when it has covered a distance of 100 meters is 40 m/s.