# A 1400 kg car traveling at a speed of 34 m/s skids to a halt on wet concrete where μk = 0.50. How long are the skid marks?

## weight = m g = 1400 * 9.81

friction force = .5 * 1400 * 9.81 = 6867 N

a = F/m = 6867/1400 = -4.9 (half a g of course)

v = 34 - 4.9 t
v = 0 at stop
so
t = 6.94 seconds
d = 34 t - (1/2)(4.9) t^2
= 34(6.94) - 2.45*6.94^2
= 236 - 118
= 118 meters

## Well, if the car skidded to a halt, I guess it must have skipped its morning coffee! Alright, let's calculate those skid marks.

First, let's find the deceleration of the car. We can use the formula:

a = μk * g

Where μk is the coefficient of kinetic friction and g is the acceleration due to gravity.

Plugging in the values, we get:

a = 0.50 * 9.8 m/s^2

a ≈ 4.9 m/s^2

Next, we can calculate the time it takes for the car to come to a stop. We can use the formula:

v = u + at

Where v is the final velocity (which is 0 m/s since the car has come to a halt), u is the initial velocity (34 m/s in this case), a is the acceleration, and t is the time.

Plugging in the values, we get:

0 = 34 + 4.9t

Solving for t, we find:

t ≈ 6.94 seconds

Finally, we can calculate the skid marks using the formula:

s = ut + (1/2)at^2

Plugging in the values:

s = 34 * 6.94 + (1/2) * 4.9 * (6.94)^2

s ≈ 166.47 meters

So, the skid marks are approximately 166.47 meters long. Just remember, it's a good thing clowns aren't driving this car, or else those skid marks would be made of banana peels and confetti!

## To find the length of the skid marks, we need to use the concept of kinetic friction.

The force of kinetic friction can be calculated using the formula:

Fk = μk * N

where Fk is the force of kinetic friction, μk is the coefficient of kinetic friction, and N is the normal force.

The normal force can be calculated using:

N = m * g

where m is the mass of the car and g is the acceleration due to gravity (approximately 9.8 m/s²).

In this case, the car is skidding to a halt, which means the force of kinetic friction is acting in the direction opposite to the motion of the car. The force of kinetic friction will work to decelerate the car until it comes to a stop.

To calculate the force of kinetic friction, we can use Newton's second law of motion:

Fk = m * a

where a is the acceleration of the car.

Since the car is skidding to a halt, the final velocity (v) will be zero, and the initial velocity (u) will be the given speed of 34 m/s. The acceleration can be calculated using the equation:

v² = u² + 2as

where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled (skid marks).

Setting v = 0 and rearranging the equation, we have:

0 = 34² + 2a * s

Now we have two equations:

Fk = μk * N
Fk = m * a

We can equate these two equations:

μk * N = m * a

Substituting the values we know:

μk * m * g = m * a

Simplifying:

μk * g = a

Now we have two equations:

0 = 34² + 2 * a * s
μk * g = a

Substituting the value of μk (0.50) and g (9.8 m/s²) into the second equation, we can solve for a:

0.50 * 9.8 = a

a ≈ 4.9 m/s²

Now we can substitute the value of a into the first equation and solve for s:

0 = 34² + 2 * 4.9 * s

1156 = 9.8 * s

s ≈ 118 meters

Therefore, the skid marks will be approximately 118 meters long.

## vf^2=vo^2-1/2 *.4*1400*9.8*d

solve for d, given vf=0