An object starts from rest an under a constant acceleration has traveled a displacement of 30.5 meters when it reaches a certain final velocity. The same object starts from rest, but has an acceleration which is a factor of 3.3 times smaller than the original acceleration. If the object reaches the same final velocity as the first acceleration reached, what would the new displacement be
To find the new displacement, we can use the kinematic equation that relates displacement to initial velocity, final velocity, and acceleration:
d = (vf^2 - vi^2) / (2a)
Let's calculate the original displacement first. We know that the initial velocity (vi) is 0 since the object starts from rest, and the final velocity (vf) is the final velocity reached by the object. Let's call the original acceleration "a1". So, we have:
d1 = (vf^2 - 0^2) / (2a1)
30.5 = (vf^2 - 0) / (2a1)
30.5 = vf^2 / (2a1)
Now, let's consider the new scenario where the acceleration is 3.3 times smaller. The new acceleration (a2) can be calculated by dividing the original acceleration (a1) by 3.3:
a2 = a1 / 3.3
Since the object still reaches the same final velocity, we can say that the final velocity in the new scenario (vf2) is equal to the final velocity in the original scenario (vf). Now, we can calculate the new displacement (d2) using the same equation but with the new values of acceleration and final velocity:
d2 = (vf^2 - 0^2) / (2a2)
d2 = vf^2 / (2(a1/3.3))
To find d2, we need to substitute the expression for a2:
d2 = vf^2 / (2(a1/3.3))
d2 = vf^2 / (2a1/3.3)
d2 = vf^2 * (3.3 / (2a1))
Therefore, the new displacement (d2) is equal to the original displacement (d1) multiplied by 3.3:
d2 = 3.3 * 30.5
d2 ≈ 100.65 meters
So, the new displacement would be approximately 100.65 meters.