Solving a Drunk Driver's Collision Problem

[DevilishNole]

Hey, I was wondering if anyone could help me with this problem:

You are the juror of a case involving a drunken driver whose 1026.0 kg sports car ran into a stationary 1913.0 kg station wagon stopped at a red traffic light. The cars stuck together and slid with locked wheels for 12.0 m before coming to rest. The coefficient of sliding friction on the dry road was 0.6. Estimate the speed of the sports car when it hit the station wagon.

I was able to figure out that the answer is equal to 34.03 m/s. However, the second part of the problem has me confused:

Estimate the instantaneous acceleration of the sports car during the actual collision if the colliding cars reach the same final speed after collapsing a combined total distance of 1.0 m.

I used the equation vf^2=vi^2+ 2a(change in x) and solved for a. For vf I used the velocity I got for the final velocity of the two cars after the collision (since it's an inelastic collision) and I got vi=0 because the station wagon was at rest. For the "change in x" I plugged in 1 m. I can't seem to get the answer, can anyone help me please?

 

[Loren Booda]

Are you considering energy of friction?

Where are your masses in the energy equation?

 

[m2003]

I would approach this problem by first clarifying the assumptions and limitations of the given information. It is important to note that this is a simplified scenario and does not accurately reflect a real-life collision, as there are many variables and factors that can affect the outcome. Additionally, it is important to consider the ethical implications of using a real-life situation for a scientific problem.

That being said, let's address the problem at hand. The first part of the problem involves calculating the initial velocity of the sports car before it collided with the stationary station wagon. This can be done by using the conservation of momentum equation, which states that the total momentum before the collision is equal to the total momentum after the collision. In this case, we can set up the equation as follows:

(m1v1) + (m2v2) = (m1+m2)vf

Where m1 and m2 are the masses of the two cars, v1 and v2 are their initial velocities, and vf is their final velocity after the collision. Plugging in the given values, we get:

(1026.0 kg)(v1) + (1913.0 kg)(0 m/s) = (1026.0 kg + 1913.0 kg)(34.03 m/s)

Solving for v1, we get v1 = 57.83 m/s, which is the initial velocity of the sports car before the collision.

Moving on to the second part of the problem, we are asked to estimate the instantaneous acceleration of the sports car during the actual collision. To do this, we can use the equation for average acceleration:

a = (vf - vi)/t

Where vf is the final velocity, vi is the initial velocity, and t is the time it takes for the cars to reach the same final speed. We know that the final velocity of both cars after the collision is 34.03 m/s, and we can assume that the time it takes for them to reach this speed is the same as the time it takes for them to collapse a combined distance of 1.0 m. Therefore, we can set up the equation as follows:

a = (34.03 m/s - 57.83 m/s)/t

We need to find the value of t, which can be calculated by using the equation for distance:

d = (vi + vf)/2 * t

Where d is the distance, vi