In this case, we are dealing with a problem related to friction and kinematics. The key is to use the information you provided to calculate the distance an object travels before coming to a stop due to friction.

Given Data:

• Mass of the object ($m$) = 10 kg
• Force of friction ($F_f$) = 20 N
• Initial velocity ($v_i$) = 0 m/s (at rest)
• Final velocity ($v_f$) = 0 m/s (stops)

Step 1: Determine the acceleration due to friction

The force of friction is responsible for decelerating the object. The equation for frictional force is:

$F_f = m \cdot a$

Where:

• $F_f$ is the frictional force
• $m$ is the mass of the object
• $a$ is the acceleration (or deceleration in this case)

Rearranging the equation to solve for acceleration $a$:

$a = \frac{F_f}{m}$

Substitute the values:

$a = \frac{20\ \text{N}}{10\ \text{kg}} = 2\ \text{m/s}^2$

Since friction is decelerating the object, the acceleration will be negative:

$a = -2\ \text{m/s}^2$

Step 2: Use kinematic equation to find the distance

Now, we will use one of the kinematic equations to find the distance. The equation that relates initial velocity, final velocity, acceleration, and distance is:

$v_f^2 = v_i^2 + 2a \cdot d$

Where:

• $v_f$ is the final velocity (0 m/s since the object stops)
• $v_i$ is the initial velocity (0 m/s)
• $a$ is the acceleration ($-2\ \text{m/s}^2$)
• $d$ is the distance

Rearranging to solve for distance $d$:

$d = \frac{v_f^2 - v_i^2}{2a}$

Substituting the values:

$d = \frac{0^2 - 0^2}{2 \times (-2)}$

$d = \frac{0}{-4} = 0\ \text{m}$

Wait, this doesn’t make sense! Let's see where we went wrong. Since $v_f$ = 0 is still approaching