Velocity of a vehicle through a skid

In summary, the conversation discusses the acceleration of a car and the use of trapezoid areas to find the change in velocity over a given time interval. The solution to finding the change in velocity is -1.8 m/s and the initial velocity of the car is 12.6 m/s. The conversation also touches on using trapezoid areas for each interval and clarifies how to solve for the initial velocity in one of the questions.
  • #1
purplemonkey
3
1
I feel a bit silly for asking for advice with this solution since it is so basic however for the life of me I can't seem to get the answer.

1. Homework Statement


A car skids to a stop. The acceleration of a car is reported in discrete times shown below: (hint, use trapezoid areas)

t (s) a (m/s/s)
0.0 -2.0
0.4 -7.0
0.8 -6.0
1.2 -5.5
1.6 -6.0
2.0 -6.0
2.4 0.0

a) What was the change in velocity over the interval t[0.0, 0.4]?
b) How fast was the car originally going?
c) What is the average acceleration of the skid?
d) How far did the vehicle skid?

Solutions:

a) I plotted these points, found the equation of the acceleration curve from t = 0 - 0.4 to be a(t) = -12.5t - 2. I then integrated that equation over the given time interval to get my change in velocity as -1.8 m/s. This solution is correct according to the answer key.

The answer to b is 12.6 m/s. However I am more interested in the solution and how that answer was achieved since I am scratching my head on this one.All others I am confident to tackle on my own.
 
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  • #2
purplemonkey said:
I
a) I plotted these points, found the equation of the acceleration curve from t = 0 - 0.4 to be a(t) = -12.5t - 2. I then integrated that equation over the given time interval to get my change in velocity as -1.8 m/s.
It would have been easier to use trapezoid areas, as suggested.

Can't you repeat this for all intervals?
 
  • #3
^^ agreed. I had initially thought to do this but I wanted to do it both ways to reaffirm the relationship between the acceleration and velocities. I plan on using the trapezoidal area method to calculate the average acceleration of the skid however I am still unclear how to solve for Vo in (b) using the information I have. :\
 
  • #4
purplemonkey said:
I plan on using the trapezoidal area method to calculate the average acceleration of the skid
My point is that you can use the trapezoid method for each interval.

purplemonkey said:
however I am still unclear how to solve for Vo in (b) using the information I have. :\
I repeat my question: can't you repeat the calculation you did in (a) for each interval?
 
  • #5
DrClaude said:
My point is that you can use the trapezoid method for each interval.I repeat my question: can't you repeat the calculation you did in (a) for each interval?
I totally missed the concept that the area under the COMPLETE curve for acceleration gives you the difference in velocity...ie if the change in velocity from the start of the braking maneuver to when the car skidded to a STOP (Vf = 0) is X m/s. Then V0 = x m/s. I feel ashamed. lol. :sorry:

Thank you for the help!
 
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What is the velocity of a vehicle through a skid?

The velocity of a vehicle through a skid is the speed at which the vehicle is moving while it is sliding or slipping on the road surface. It is typically measured in miles per hour (mph) or kilometers per hour (km/h).

How is the velocity of a vehicle through a skid calculated?

The velocity of a vehicle through a skid is calculated by dividing the distance traveled during the skid by the time it took for the skid to occur. This calculation is based on the formula v=d/t, where v is velocity, d is distance, and t is time.

What factors affect the velocity of a vehicle through a skid?

There are several factors that can affect the velocity of a vehicle through a skid, including the speed of the vehicle, the type and condition of the road surface, the weight and distribution of the vehicle's load, and the type and quality of the vehicle's tires.

How does the velocity of a vehicle through a skid impact safety?

The velocity of a vehicle through a skid can greatly impact safety, as a higher velocity means a longer stopping distance and less control over the vehicle. It is important for drivers to maintain a safe and appropriate speed to avoid skidding and maintain control of the vehicle.

What can be done to reduce the velocity of a vehicle through a skid?

To reduce the velocity of a vehicle through a skid, drivers can take several precautions such as maintaining an appropriate speed, avoiding sudden or sharp turns, and keeping a safe distance from other vehicles. It is also important to regularly maintain and check the tires, brakes, and other components of the vehicle to ensure safe driving conditions.

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