Velocity of a vehicle through a skid

[purplemonkey]

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.

 

[DrClaude]

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?

 

[purplemonkey]

^^ 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. :\

 

[DrClaude]

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.

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?

 

[purplemonkey]

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.

Thank you for the help!