1.3 Iridov - Find Time Interval ( Kinematics )

[razored]

Thank you for taking the time to read this lengthy post.

A car starts moving rectilinearly, first with acceleration a=5m/s2(the initial velocity is 0) then uniformly, and finally, decelerating at the same rate a, comes to stop.The total time of motion equals 25 seconds. The average velocity during whole time is 72 km/h. How long does the car move uniformly?


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http://img26.imageshack.us/img26/1403/defaultx.png" [Broken]


All my equations appear to be correct; however, when I calculate the t_{o}, I get an imaginary answer. What did I miss or do wrong?

 

[LowlyPion]

Thank you for taking the time to read this lengthy post.

A car starts moving rectilinearly, first with acceleration a=5m/s2(the initial velocity is 0) then uniformly, and finally, decelerating at the same rate a, comes to stop.The total time of motion equals 25 seconds. The average velocity during whole time is 72 km/h. How long does the car move uniformly?

Maybe consider the area of a trapezoid?

That is what your V_(t) graph represents.

You know that the integral of V_(t) yields X_(t)

They tell you what the area is ... avg V * total T = 20 * 25 = 500.

The base is 25 sec and total X is 500
So ...

(25+X)/2*H = 500

You also know that X = 25 - 2d
where d is the 2 periods of acceleration and deceleration.

And H = 5*d
where V = 5*t so ...

H = 5*(25 -X)/2

Combining things then yields:

5*(25 -X)/2*(25+X)/2 = 500

5/4*(25² - X²) = 500

I get a real result.

 

[razored]

Actually, I ignored the graph I drew when I solved the problem because I realized(on another piece of paper) that the area I was calculating (two triangles and rectangle) was identical to D = 2x_o + x_1.

This may be asking too much but can you find the mistake in my work? I just don't see it.

Thanks again.

 

[LowlyPion]

Actually, I ignored the graph I drew when I solved the problem because I realized(on another piece of paper) that the area I was calculating (two triangles and rectangle) was identical to D = 2x_o + x_1.

This may be asking too much but can you find the mistake in my work? I just don't see it.

Thanks again.

Now that you know the answer, you can work backwards to figure the error in your math. In all honesty, I'm not that interested in looking.

 

[dx]

EDIT : My mistake.