Two stacked boxes are sliding along an ice rink with an initial velocity vec$(v{)}_0$ to the right. You are trying to stop the boxes so you exert a force vec$(F{)}_{Y1}$ on the top box as indicated in the figure.

The magnitude of the force that you exert is variable, and follows the equation: $F_{Y1}=F_0{e}^{-bt}$ with $F_0$ and $b$ constants, and $t$ the time since you began exerting the force.

Because the boxes are sliding on ice, the friction between box $2$ and the ground is negligible. There is friction between the two boxes, and they are observed to accelerate together as you exert the force to slow them down.

Note: This problem will be much easier if you solve everything symbolically before you substitute numerical values for the parameters.

Use the following values for the parameters:

$m_1=8\mathrm{.}6kg$

$m_2=2\mathrm{.}9kg$

$=29\mathrm{.}1$

$F_0=123N$

$b=0\mathrm{.}11s^{-1}$

$t_1=1\mathrm{.}5s$

$v_0=7\mathrm{.}6\frac{m}{s}$

Acceleration

Determine the magnitude of the common acceleration of the two boxes a time $t_1$ after you begin exerting the force. Assume that $t_1$ is before the two boxes stop.

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$a(t_1)=$

Hint:

Hint:

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Speed of Boxes

Determine the common speed of the two boxes at $t_1.$

$v_1=$

Hint:

Friction force of box $1$ on box $2$

Find the magnitude of the friction force from $1$ on $2$ at $t_1.$ You may use ${}_s=0\mathrm{.}16$ and ${}_k=0\mathrm{.}13$

$f_{21}=$

Hint:

Stopping Time

Determine the total time, $t_f,$ that it takes you to stop the blocks.

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$t_f$:

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Hint: