A skater with an initial speed of 5.90 m/s stops propelling himself and begins to coast across the ice, eventually coming to rest. Air resistance is negligible.

(a) The coefficient of kinetic friction between the ice and the skate blades is 0.125. Find the deceleration caused by kinetic friction.
(b) How far will the skater travel before coming to rest?

To find the deceleration caused by kinetic friction, we can use the formula:

Acceleration due to friction = coefficient of friction * acceleration due to gravity

Given:
Initial speed of the skater (u) = 5.90 m/s
Coefficient of kinetic friction (μ) = 0.125

Acceleration due to gravity (g) = 9.8 m/s² (standard value)

(a) To find the deceleration caused by kinetic friction:

Acceleration due to friction = 0.125 * 9.8 = 1.225 m/s²

Therefore, the deceleration caused by kinetic friction is 1.225 m/s².

(b) To find the distance the skater will travel before coming to rest, we can use the formula:

Distance (s) = (Initial velocity² - Final velocity²) / (2 * acceleration)

Given:
Initial velocity (u) = 5.90 m/s
Final velocity (v) = 0 m/s (since the skater comes to rest)
Acceleration (a) = -1.225 m/s² (negative sign denoting deceleration)

Plugging in these values into the formula:

Distance (s) = (5.90² - 0²) / (2 * -1.225)

Simplifying:

Distance (s) = 34.81 / -2.45

Distance (s) = -14.204 m

Since distance cannot be negative, we consider the magnitude:

Distance (s) = 14.204 m

Therefore, the skater will travel approximately 14.204 meters before coming to rest.