Complete Question
The complete question is shown on the first uploaded image
Answer:
The distance which the car skid is [tex]l = \frac{v_i^2 }{2 * \mu_k * g }[/tex]
Explanation:
From the question we are told that
The initial velocity of the car is [tex]v_i[/tex]
The coefficient of kinetic friction is [tex]\mu_k[/tex]
According to the law of energy conservation
The initial Mechanical Energy = The final Mechanical Energy
[tex]M_i = M_f[/tex]
The initial mechanical energy is mathematically represented as
[tex]M_i = KE _o + PE_e[/tex]
where KE is the initial kinetic energy which is mathematically represented as
[tex]KE = \frac{1}{2} m v_i^2[/tex]
And PE is the initial potential energy which is zero given that the car is on the ground
Now
[tex]M_f = W_{\mu}[/tex]
Where [tex]W_{\mu}[/tex] is the work which friction exerted on the car which is mathematically represented as
[tex]W_{\mu} = m* \mu_k * g * l[/tex]
Where [tex]l[/tex] is the distance covered by the car before it slowed down
[tex]\frac{1}{2} m v_i^2 = m* \mu_k * g * l[/tex]
=> [tex]l = \frac{v_i^2 }{2 * \mu_k * g }[/tex]
