Was the Car Speeding Based on Skid Mark Analysis?

[Elo21]

Homework Statement

you are a crime scene specialists. a car in an accident had skidded to a stop and left tire tracks for 32 meters. The coefficient of sliding friction between the tires and road is .45, and the car's mass is 1000kg. Was the driver exceeding 25mph (11.3m/s) speed limit?

Homework Equations

u= Force Friction / Normal Force
F net= m*a

I can't figure it out because i don't think i know all the formulas i need to know.

The Attempt at a Solution

I tried but it is to much to write.

 

[mgb_phys]

Welcome to pf.

You know the friction force acting to slow the car.
So you can either use F=ma to work out the acceleration and what initial speed it would need to take that distance to stop.
Or you know energy= force * distance, work out how much energy you lost to friction over that distance and what initial kinetic energy (and so speed) you must have had.

 

[Cryxic]

Homework Statement

you are a crime scene specialists. a car in an accident had skidded to a stop and left tire tracks for 32 meters. The coefficient of sliding friction between the tires and road is .45, and the car's mass is 1000kg. Was the driver exceeding 25mph (11.3m/s) speed limit?

Homework Equations

u= Force Friction / Normal Force
F net= m*a

I can't figure it out because i don't think i know all the formulas i need to know.

The Attempt at a Solution

I tried but it is to much to write.

The first objective is to determine the car's deceleration. After that, we use kinematics to calculate the car's initial velocity and compare it to the speed limit.

The frictional force acting against the car's motion can be written as:

$$F_f = u_kF_N$$

The normal force is mg, so the equation becomes:

$$F_f = u_kmg$$

We can reduce this equation to:

$$ma_f = u_kmg$$

where, after canceling the masses from both sides, we have:

$$a_f = u_kg$$

so

$$a_f = - 4.41 m/s^2$$

Now plug this into the kinematics equation:

$$v_f^2 = v_i^2 + 2a_fx$$

Final velocity is 0. Just solve for the initial velocity and you should get around 17 m/s. The driver was speeding.

 

[Elo21]

thank you.

 

[berkeman]

The first objective is to determine the car's deceleration. After that, we use kinematics to calculate the car's initial velocity and compare it to the speed limit.

The frictional force acting against the car's motion can be written as:

$$F_f = u_kF_N$$

The normal force is mg, so the equation becomes:

$$F_f = u_kmg$$

We can reduce this equation to:

$$ma_f = u_kmg$$

where, after canceling the masses from both sides, we have:

$$a_f = u_kg$$

so

$$a_f = - 4.41 m/s^2$$

Now plug this into the kinematics equation:

$$v_f^2 = v_i^2 + 2a_fx$$

Final velocity is 0. Just solve for the initial velocity and you should get around 17 m/s. The driver was speeding.

Please do not do the OP's homework for them. That's not how the Homework Help forums work here at the PF.