A stone falls freely from rest for 8.0s.

A. Calculate the stone's velocity after 8.0s.

V2-V1+at
V2 = (0) = 9.8(8.0)
V2 = 78.4m/s

B. What is the stone's displacement during this time?

d = (v2 + v1)t/2
d = (78.4 + 0)/2(8.0)
d = 313.6m

You seem to be mixing up your = and - signs in the first two equations. Those were probably just typing errors.

I agree with your answers.

Well, if the stone falls freely for 8.0 seconds, it must have really wanted to make it to the ground. Talk about dedication!

A) The velocity of the stone after 8.0 seconds is 78.4 m/s. It's like the stone took a shortcut to superhero speed!

B) During this time, the stone displaces a distance of 313.6 meters. That's quite the leap of faith! It's probably auditioning for the next Olympic long jump competition.

To calculate the stone's velocity after 8.0s, we can use the equation V2 = V1 + at, where V1 is the initial velocity (which is 0 since it falls from rest), a is the acceleration due to gravity (which is approximately 9.8 m/s^2), and t is the time (which is 8.0s).

Plugging in the values, we get:

V2 = 0 + (9.8 m/s^2)(8.0s)
V2 = 78.4 m/s

Therefore, the stone's velocity after 8.0s is 78.4 m/s.

To calculate the stone's displacement during this time, we can use the equation d = (V2 + V1)t/2, where d is the displacement, V2 is the final velocity (which is 78.4 m/s), V1 is the initial velocity (which is 0 since it falls from rest), and t is the time (which is 8.0s).

Plugging in the values, we get:

d = (78.4 m/s + 0 m/s)(8.0s)/2
d = (78.4 m/s)(8.0s)/2
d = (627.2 m·s)/2
d = 313.6 m

Therefore, the stone's displacement during this time is 313.6 m.

To calculate the velocity of the stone after 8.0 seconds, you can use the formula V2 = V1 + at, where V2 is the final velocity, V1 is the initial velocity, a is the acceleration (which is equal to the acceleration due to gravity, approximately 9.8 m/s^2), and t is the time.

In this case, the stone starts from rest, so the initial velocity (V1) is 0. Substituting this information into the formula, you can calculate the final velocity (V2):

V2 = (0) + (9.8)(8.0)
V2 = 78.4 m/s

Therefore, the stone's velocity after 8.0 seconds is 78.4 m/s.

To calculate the stone's displacement during this time, you can use the formula d = (V2 + V1)t / 2, where d is the displacement, V2 is the final velocity, V1 is the initial velocity, and t is the time.

Since the stone starts from rest, the initial velocity (V1) is 0. Substituting the given values into the formula, you can calculate the displacement (d):

d = (78.4 + 0) / 2(8.0)
d = 313.6 m

Therefore, the stone's displacement during this time is 313.6 meters.