How to find velocity given coefficient of friction, distance, mass and v1?

[Ingrid44]

Homework Statement

calculate the final velocity of an object sliding across a surface with a coefficient of friction of 0.2, a distance of 3m, an initial velocity of 50m/s and the object's mass of 100kg.
μ=0.2
v1= 50m/s
d=3m
m=100kg
v2= ?

Homework Equations

I know
F= μ*normal force (mg)
Kinetic Energy= 1/2mv^2

The Attempt at a Solution

I am confused and can't see how to get to the answer. Sorry, its been long since I took physics, I will really appreciate some help. Just the process of getting there. THANK YOU :)

 

[diazona]

Here are a couple more equations for you:

$$W = Fd$$

$$W = \Delta K$$
(K is kinetic energy)

Does that help?

 

[nlightner]

To find the final velocity of an object sliding across a surface, we can use the equation: v2^2 = v1^2 + 2ad - 2μmgd.

First, we need to find the normal force (N) acting on the object, which is equal to the object's weight (mg) multiplied by the coefficient of friction (μ). So, N = μmg = 0.2 * 100kg * 9.8m/s^2 = 196N.

Next, we can plug in the given values into the equation: v2^2 = (50m/s)^2 + 2(0.2)(100kg)(9.8m/s^2)(3m) - 2(0.2)(100kg)(9.8m/s^2)(3m).

Simplifying, we get v2^2 = 2500m^2/s^2 + 1176m^2/s^2 - 1176m^2/s^2 = 2500m^2/s^2.

Taking the square root of both sides, we get v2 = √2500m^2/s^2 = 50m/s.

Therefore, the final velocity of the object is 50m/s.