Question

Police investigators, examining the scene of an accident involving two cars, measure 72-mlong skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.

Answer 1

To estimate the initial speed of the car involved in an accident, the work-energy principle is used, with the work done by friction equated to the initial kinetic energy. By using the coefficient of kinetic friction and the length of the skid marks, the initial speed can be determined without needing the car's mass.

Step-by-step explanation:

To estimate the initial speed of the car before the collision, we can use the work-energy principle, which states that the work done by the forces on the car is equal to the change in kinetic energy. In this case, the only significant force at work is friction, which we can calculate using the coefficient of kinetic friction (μ) and the length of the skid marks (d).

The formula for work done by friction (W) is W = μ * m * g * d, where m is the mass of the car, g is the acceleration due to gravity, and d is the distance. However, since the mass of the car is not provided, we will use the fact that the frictional force (f) is equal to μ * m * g and do not need to know the mass of the vehicle for this calculation.

The initial kinetic energy (KE_initial) would be ½*m*v², where v is the initial speed of the car. Since the car nearly came to a stop, final kinetic energy (KE_final) is 0, so the work done by friction is equal to the initial kinetic energy.

Setting these equal and solving for v, the equation simplifies to v = √(2*μ*g*d). Plugging in the values, we have μ = 0.80 and d = 72 m, with g roughly equal to 9.81 m/s² (the acceleration due to gravity). Therefore, v = √(2*0.80*9.81 m/s²*72 m).

After calculating the above expression, we can estimate the initial speed of the car before it began to skid.

Answer 2

The initial speed of car is 33.6
`(m)/(s)`

Step-by-step explanation:

Given :

Distance travel by cars
`x = 72` m

Coefficient of kinetic friction
`\mu _(k) = 0.80`

From the equation of kinematics,

`v^(2) - v_(o) ^(2) = 2ax`

Where
`v_(o) =` final speed here it is zero (
`v_(o) = 0` ),
`a =` acceleration of car

From FBD diagram we can write,

`ma =- \mu _(k) mg`

Here minus sign represent friction oppose the motion,

`a = -\mu_(k) g`

`a = -7.84 (m)/(s^(2) )` ( ∵
`g = 9.8 (m)/(s^(2) )` )

Put the value of acceleration in above equation and find initial velocity,

`v_(o)^(2) = -2 * (-7.84) * 72`

`v_(o)^(2) = 1128.96`

`v_(o)^{} = 33.6`
`(m)/(s)`

Therefore, the initial speed of car is 33.6
`(m)/(s)`