* At an accident scene on a level road, investigators measure a car's skid mark to be 58 m long. It was a rainy day and the coefficient of friction was estimated to be 0.38. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes.

I can not figure out which formulas to use for this problem or how to solve it.

To answer this question you must first solve:

Acceleration=(gravity)(coefficient of friction) which equals 3.724
you than plug acceleration into the equation (velocity final)^2=(velocity initial)^2+2(acceleration)(distance)
and you solve for velocity initial:
(0)^2=(VI)^2+2(-3.724)(58)
-(VI^2)=-(431.9)
(VI^2)=431.9
VI= 20.7842 m/s
Hope that this helps

I have not understood where the negative came from...

how is this coming "2(acceleration)(distance)"

To determine the speed of the car when the driver slammed on the brakes, you can use the principles of mechanical energy and the relationship between friction force, coefficient of friction, and normal force.

Here are the step-by-step instructions to solve the problem:

Step 1: Identify the known variables:
- Skid mark length (s) = 58 m
- Coefficient of friction (μ) = 0.38

Step 2: Determine the acceleration due to friction:
Since the car is on a level road, the net force acting in the horizontal direction is the force of friction. The friction force (Ff) can be determined using the formula:
Ff = μ * N

However, the normal force (N) is equal to the weight (mg) of the car, where m is the mass of the car and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Step 3: Calculate acceleration:
From the above, we can write:
Ff = μ * N
ma = μ * mg

Rearranging the equation to solve for acceleration (a):
a = μ * g

Substituting the known values:
a = 0.38 * 9.8 m/s^2

Step 4: Calculate initial velocity (Vi):
In this scenario, the car's initial velocity is unknown. However, we know that the car started from rest before the brakes were applied. Hence, the initial velocity (Vi) is 0 m/s.

Step 5: Use the kinematic equation to solve final velocity (Vf):
The kinematic equation relating initial velocity (Vi), final velocity (Vf), acceleration (a), and distance (s) is:
Vf^2 = Vi^2 + 2as

Rearranging the equation to solve for final velocity (Vf):
Vf = sqrt(Vi^2 + 2as)

Substituting the known values and rearranging the equation:
Vf = sqrt(0 + 2 * a * s)
Vf = sqrt(2 * a * s)

Step 6: Calculate the final velocity (Vf):
Vf = sqrt(2 * 0.38 * 9.8 * 58)

Calculate the value using a calculator:
Vf ≈ 26.79 m/s

Therefore, the speed of the car when the driver locked the brakes was approximately 26.79 m/s.

To solve this problem, we can use the physics equation that relates the coefficient of friction, the length of skid marks, and the initial velocity of the car.

The equation is:

(v^2) = (u^2) + 2as

Where:
v = final velocity of the car (which is 0 m/s since it came to a complete stop)
u = initial velocity of the car (what we're trying to find)
a = acceleration of the car (which we can calculate using the coefficient of friction)
s = length of the skid marks (given as 58 m)

First, let's calculate the acceleration (a) using the coefficient of friction.

The equation for acceleration due to friction is:

a = μg

Where:
μ = coefficient of friction (given as 0.38)
g = acceleration due to gravity (approximately 9.8 m/s^2)

Substituting the values, we get:

a = 0.38 * 9.8

Next, we plug in the values of a, v, and s into the first equation:

(0^2) = (u^2) + 2 * a * s

Simplifying further, we get:

0 = (u^2) + 2 * (0.38 * 9.8) * 58

Now we can solve for u by rearranging the equation:

(u^2) = -2 * (0.38 * 9.8) * 58

Taking the square root of both sides, we get:

u = √[-2 * (0.38 * 9.8) * 58]

Evaluating the right-hand side of the equation, we find:

u ≈ -√1134.56

Since velocity cannot be negative in this context, we can conclude that the initial velocity of the car (u) is approximately 33.68 m/s when the driver slammed on the brakes.

Please note that this calculation assumes the car came to a complete stop and that the skid marks were produced by the locked brakes. Additionally, this answer is based on the given data and assumptions and may not accurately represent the actual situation.