Question

B. A car moving at an initial speed vi applies its brakes and skids for some distance until coming to a complete stop. If the coefficient of kinetic friction between tires and the road is µk what distance did the car skid?

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

The distance which the car skid is
`l = (v_i^2 )/(2 * \mu_k * g )`

Step-by-step explanation:

From the question we are told that

The initial velocity of the car is
`v_i`

The coefficient of kinetic friction is
`\mu_k`

According to the law of energy conservation

The initial Mechanical Energy = The final Mechanical Energy

`M_i = M_f`

The initial mechanical energy is mathematically represented as

`M_i = KE _o + PE_e`

where KE is the initial kinetic energy which is mathematically represented as

`KE = (1)/(2) m v_i^2`

And PE is the initial potential energy which is zero given that the car is on the ground

Now

`M_f = W_(\mu)`

Where
`W_(\mu)` is the work which friction exerted on the car which is mathematically represented as

`W_(\mu) = m* \mu_k * g * l`

Where
`l` is the distance covered by the car before it slowed down

`(1)/(2) m v_i^2 = m* \mu_k * g * l`

=>
`l = (v_i^2 )/(2 * \mu_k * g )`