A kitten pushes a ball of yarn rolling toward it at 1.00 cm/s with its nose, displacing the ball of yarn 17.5 cm in the opposite direction in 2.00 s. What is the acceleration of the ball of yarn?
I would just use x = (vi)t + 1/2 (a)(t^2)
and remember that vi is -1.
conyo
To find the acceleration of the ball of yarn, we can use the equation:
acceleration = (change in velocity) / time
First, let's find the change in velocity. The initial velocity is zero because the ball of yarn is at rest. The final velocity can be determined using the displacement and time given:
displacement = initial velocity * time + (1/2) * acceleration * time^2
In this case, the initial velocity is zero, so the equation simplifies to:
displacement = (1/2) * acceleration * time^2
Rearranging the equation, we get:
acceleration = (2 * displacement) / (time^2)
Now, let's plug in the given values:
displacement = -17.5 cm (since the displacement is in the opposite direction)
time = 2.00 s
acceleration = (2 * (-17.5 cm)) / (2.00 s)^2
Before we proceed, we need to convert the displacement to meters and the time to seconds:
displacement = -17.5 cm = -0.175 m
time = 2.00 s
acceleration = (2 * (-0.175 m)) / (2.00 s)^2
Simplifying further:
acceleration = (-0.35 m) / (4 s^2)
Therefore, the acceleration of the ball of yarn is -0.0875 m/s^2. The negative sign indicates that the acceleration is in the opposite direction of the ball's motion.