91Ó°ÊÓ

Kinematics can be defined as the branch of science that describes how objects move.

It is essential for describing an end-effector's position, orientation, and motion of all joints. It also includes the calculation of the trajectory of particles.

Given data:

The mass of the ice skater is $m=65\mathrm{kg}$.

The displacement is $s=75\mathrm{m}$.

The coefficient of kinetic friction is ${\mathrm{μ}}_{\mathrm{k}}=0.10$.

Draw a free body diagram.

Here, $F_{\mathrm{fr}}$is the frictional force, $F_{\mathrm{N}}$is the normal force, and$g$ is the acceleration due to gravity.

As she travels with no effort for a distance of 75 m, the only force acting on her is the force of friction.

Apply the equilibrium condition along the horizontal direction.

$\begin{array}{c}∑F_{\mathrm{x}}=ma\\ -F_{\mathrm{fr}}=ma\\ -{\mathrm{μ}}_{\mathrm{k}}mg=ma\\ a=-{\mathrm{μ}}_{\mathrm{k}}g\end{array}$

Substitute the values in the above expression.

$\begin{array}{l}a=-\left(0.10\right)\left(9.8\mathrm{m}{/\mathrm{s}}^2\right)\\ a=-0.98\mathrm{m}{/\mathrm{s}}^2\end{array}$

Here, a negative sign indicates deceleration.

As she stops at the final position, her final velocity will be $v=0$.

The initial velocity of the ice skater can be calculated as:

$\begin{array}{c}{v}^2=u^2+2as\\ \left(0\right)={\left(u\right)}^2+2\left(-0.98\mathrm{m}{/\mathrm{s}}^2\right)\left(75\mathrm{m}\right)\\ u=12.12\mathrm{m}/\mathrm{s}\end{array}$

Thus, the initial velocity of the ice skater is$12.12\mathrm{m}/\mathrm{s}$.