Final answer:
To find the distance the box will slide when it has slowed down to 5.20 m/s, you need to calculate the deceleration of the box and then use the kinematic equation. The deceleration can be calculated using the coefficient of kinetic friction, and then the distance can be calculated using the kinematic equation. Substitute the given values to find the final answer.
Step-by-step explanation:
To find the distance the box will slide when it has slowed down to 5.20 m/s, we need to calculate the deceleration of the box and then use the kinematic equation. The deceleration of the box can be calculated using the coefficient of kinetic friction:
Deceleration = coefficient of kinetic friction * g
where g is the acceleration due to gravity. Once we have the deceleration, we can use the kinematic equation:
V^2 = U^2 + 2aS
where V is the final velocity (5.20 m/s), U is the initial velocity (8.40 m/s), a is the deceleration, and S is the distance the box will slide. Rearranging the equation, we have
S = (V^2 - U^2) / (2a)
Substituting the given values, we get:
S = (5.20^2 - 8.40^2) / (2 * deceleration)
Now, we can substitute the value of the deceleration and calculate the final answer.