A body starting from rest travels for 30s detemine the final velo city attainet atter covering adistance of 40m
Answer me
To determine the final velocity attained by a body after traveling a distance of 40m for 30s, we can use the kinematic equation:
v^2 = u^2 + 2as
where:
v = final velocity
u = initial velocity (which is 0 m/s since the body starts from rest)
a = acceleration
s = distance
Given:
u = 0 m/s
s = 40 m
t = 30 s
First, we can calculate the acceleration using the formula:
a = (v - u) / t
Since the initial velocity is 0 m/s, the formula simplifies to:
a = v / t
Substituting the given values:
a = v / 30
Next, substituting the values of u, a, and s into the kinematic equation:
v^2 = 0^2 + 2 * a * s
v^2 = 2 * a * s
v^2 = 2 * (v / 30) * 40
Solving for v:
v^2 = (2 * 40 * v) / 30
v^2 = (80 * v) / 30
30 * v^2 = 80 * v
30v^2 = 80v
Divide both sides by v:
30v = 80
v = 80 / 30
v ≈ 2.67 m/s
Therefore, the final velocity attained after covering a distance of 40m for 30s is approximately 2.67 m/s.
To determine the final velocity attained by a body starting from rest and traveling for 30 seconds to cover a distance of 40 meters, we can use the formula for calculating final velocity given initial velocity, acceleration, and time:
v = u + at
In this case, the body starts from rest, so the initial velocity (u) is 0 m/s. We also know the time (t), which is 30 seconds. However, we need to find the acceleration (a) in order to calculate the final velocity (v).
To find the acceleration, we can use the equation:
s = ut + (1/2)at^2
where s is the distance traveled. We know that s = 40 meters, u = 0 m/s, and t = 30 seconds. Plugging these values into the equation, we can solve for a:
40 = 0*(30) + (1/2)*a*(30)^2
Simplifying the equation:
40 = 450a
Dividing both sides by 450:
a = 40/450
a ≈ 0.0889 m/s^2
Now that we have the acceleration, we can use the first equation to find the final velocity:
v = u + at
v = 0 + (0.0889)*(30)
v ≈ 2.667 m/s
Therefore, the final velocity attained by the body after covering a distance of 40 meters in 30 seconds is approximately 2.667 m/s.