91Ó°ÊÓ

The acceleration of the child on the sled can be evaluated with the help of Newton's third law. The average retarding force on the sled can be calculated by Newton's second law.

The product of the total mass and the sled's acceleration gives the retarding force on the sled.

The given data can be listed below as:

• The mass of the child and sled together is $m=60\mathrm{kg}$.
• The initial velocity of the child on the sled is $v_i=10\mathrm{m}/\mathrm{s}$.
• The distance traveled by the sled is $d=25\mathrm{m}$.
• The final velocity of the child on a sled is $v_f=0\mathrm{m}/\mathrm{s}$.

From Newton’s third law, the final velocity of the sled can be expressed as:

$\begin{array}{c}{v}_f^2=v_i^2+2ad\\ a=\frac{v_f^2-v_i^2}{2d}\end{array}$

Here, d is the distance moved by the child and the sled together, and $v_f$is the final speed of the sled. At the stop, the final speed of the sled becomes 0 m/s as the sled comes to rest.

Substitute the values as $0\mathrm{m}/\mathrm{s}$for $v_f$and $10\mathrm{m}/\mathrm{s}$for $v_i$in the above equation.

$\begin{array}{c}a=\frac{{\left(0\mathrm{m}/\mathrm{s}\right)}^2-{\left(10\mathrm{m}/\mathrm{s}\right)}^2}{2×25\mathrm{m}}\\ =-2\mathrm{m}/{\mathrm{s}}^2\end{array}$

Here, the negative sign indicates the deceleration of the sled.

Thus, the acceleration of the sled is $-2\mathrm{m}/{\mathrm{s}}^2$.

$\begin{array}{c}{v}_f^2=v_i^2+2ad\\ a=\frac{v_f^2-v_i^2}{2d}\end{array}$

From Newton’s second law, the average force on the sled can be given as:

$F=ma$

Here, m is the mass of the child and sled together, and a is the acceleration of the sled.

Substitute the values as 60 kg for m, and $\left(-2\mathrm{m}/{\mathrm{s}}^2\right)$for a in the above equation.

$\begin{array}{c}F=60\mathrm{kg}×\left(-2\mathrm{m}/{\mathrm{s}}^2\right)\\ =-60\mathrm{kg}×2\mathrm{m}/{\mathrm{s}}^2\left(\frac{1\mathrm{N}}{1\mathrm{kg}·\mathrm{m}/{\mathrm{s}}^2}\right)\\ =-120\mathrm{N}\end{array}$

Here, the negative sign indicates the retarding nature of the force and the force is acting in the opposite direction to the child’s velocity.

Thus, the average retarding force on the sled is $120\mathrm{N}$in the direction opposite to the child’s velocity.