Final answer:
To calculate the acceleration of the ball of yarn, we use the displacement equation with constant acceleration since the initial velocity is zero and the displacement and time are given. We find that the acceleration of the ball of yarn is 0.0875 m/s².
Step-by-step explanation:
To calculate the acceleration of the ball of yarn, we can use the kinematic equation for uniformly accelerated motion:
vf^2 = vi^2 + 2ad
Where vf is the final velocity, vi is the initial velocity (which is 0 since the ball starts at rest), a is the acceleration, and d is the displacement. Since we are not given the final velocity directly, we need to use another equation to find it: vf = vi + at, where t is the time taken to displace the ball. Once we have the final velocity, we can substitute back into the first equation to solve for acceleration.
To find the final velocity, with vi = 0 and t = 2 seconds, the only unknown is vf, but without final velocity, first, we are unable to calculate acceleration directly. However, we can use the equation for displacement with constant acceleration: d = vit + 0.5at^2. By substituting the known values (d = 0.175 m, vi = 0, and t = 2 s), we can solve for acceleration:
0.175 m = 0 + 0.5a(2 s)^2
0.175 m = 2a s^2
a = 0.175 m / 2 s^2
a = 0.0875 m/s^2