# 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?

Jan 22, 2018

$- 9.75 c m / {s}^{2}$

#### Explanation:

$s = u t + \frac{1}{2} a {t}^{2}$

displacement = starting velocity + ($\frac{1}{2}$ * acceleration * time^2)

acceleration is in $c m / {s}^{2}$
velocity is in $c m / s$
time is in $s$

$u = 1.00$cm/s

$t = 2.00$s

$s = - 17.5$cm (opposite direction)

$- 17.5 = \left(1 \cdot 2\right) + \frac{1}{2} \cdot a \cdot {2}^{2}$

$- 17.5 = 2 + 2 a$

$- 19.5 = 2 a$

$a = - \frac{19.5}{2}$

$a = - 9.75$

acceleration $= - 9.75 c m / {s}^{2}$