What was the initial velocity of the car?

[Schu]

It's been a while since I have gone through my physics classes so help me out if you would.

While investigating a traffic accident we found skid marks that were 24.9 m in length. The mass of the car was around 1250 kg. After the accident reconstructionist used his "sled" the coefficient of friction was 0.836. What was the initial velocity of the car?

From what I remember if unknown variable such as the time or acceleration would make this problem easy. Hopefully I will be able to go to the reconstructionist school and learn the things specific to accidents.
I'm not sure how to go about finding the velocity. Can anyone help?

 

[AKG]

You have the mass of the car. You can figure out the gravitational force. You can then figure out the normal force on the car. You can then figure out the frictional force, then the acceleration. You have the final velocity of the car and the distance travelled. Now, you can figure out the initial velocity.

 

[Schu]

gravitational force = mass * gravity
normal force = gravitational force
friction force = coefficient of friction * Normal Force
sum of the forces = mass * acceleration?? What forces do you add up, the vertical or the horizontal or both? I had gone down this road but this last part confused me.

 

[AKG]

gravitational force = mass * gravity
normal force = gravitational force
friction force = coefficient of friction * Normal Force
sum of the forces = mass * acceleration?? What forces do you add up, the vertical or the horizontal or both? I had gone down this road but this last part confused me.

If you know what forces are acting on the body, and know how to add vectors together, you should be fine. Tell us the forces you believe to be acting on the body in question, including magnitude and direction. In fact, if you can do that step but don't know how to sum those forces, then let us know that that is the problem, and perhaps you just need a quick reminder on vector addition.

 

[Schu]

The car was moving on a level plane in a straight direction which would be a 0 degree direction if looking on an x,y grid. The mass of the car is 1250 kg. It took the car 24.9 m to stop. The final velocity is 0 m/s the coefficient of friction was 0.836.

See if I am making any sense.
Gravitational force
1250 * (-9.81) = (-12262.5) N
Normal Force since Fg + Fn = 0
12262.5 N
Friction Force Ff= coef of friction * Fn
0.836 * 12262.5 = 10251.45N

Now I have problem adding the vectors to get the sum of the forces which prevents me from getting the acceleration. Which vectors do I add so I can put it in the Sum of FOrces = mass * acccel

 

[AKG]

The car was moving on a level plane in a straight direction which would be a 0 degree direction if looking on an x,y grid. The mass of the car is 1250 kg. It took the car 24.9 m to stop. The final velocity is 0 m/s the coefficient of friction was 0.836.

See if I am making any sense.
Gravitational force
1250 * (-9.81) = (-12262.5) N
Normal Force since Fg + Fn = 0
12262.5 N
Friction Force Ff= coef of friction * Fn
0.836 * 12262.5 = 10251.45N

Now I have problem adding the vectors to get the sum of the forces which prevents me from getting the acceleration. Which vectors do I add so I can put it in the Sum of FOrces = mass * acccel

Vector quantities require a direction. I believe I asked if you could list the forces involved with magnitude and direction.

$$\vec{F}_G = mg [down]$$

$$\vec{F}_N = mg [up]$$

$$\vec{F}_{fr} = \mu |\vec{F_N}| [back]$$

$$\vec{F}_{net} = \vec{F}_G + \vec{F}_N + \vec{F}_{fr}$$

$$= mg [down] + mg [up] + \mu mg [back]$$

$$= mg [down] - mg [down] + \mu mg [back]$$

$$= \mu mg [back]$$​

I'm sure you understand why $mg [up] = -mg [down]$. So, now I've given you $\vec{F}_{net}$, can you get the rest?

 

[Schu]

I think I am all set now. The F net = m*a correct? THen a = Sum F / m

Thanks for the help.