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?

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Answer 1 · 2018-01-22T20:50:55

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

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

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

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

$u = 1.00$ $u = 1.00$ cm/s

$t = 2.00$ $t = 2.00$ s

$s = - 17.5$ $s = -17.5$ cm (opposite direction)

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

$- 17.5 = 2 + 2 a$ $-17.5 = 2 + 2a$

$- 19.5 = 2 a$ $-19.5 = 2a$

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

$a = - 9.75$ $a = -9.75$

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