EK 1001 Physics Q57 using uniformly accelerated equations to find speed?

[silverice]

The following Exam Kracker 1001 Physics, used a Uniformly Accelerated Motion Equation on a Linear Motion. I didn't know that we can use the formulas this way. Can anyone please elaborate on the answer/explanation?

The question:
57. A particle moving at 5 m/s reverses its direction in 1 s to move at 5 m/s in the opposite direction. If its acceleration is constant, what is its speed at 0.5 s?

Answer: 0 m/s
Explanation: Use V=Vo+at, where a=(Vfinal-Vinitial)/t, but use 1/2 for t in the first equation because we want the speed halfway through the trip.

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[SKaminski]

The equation also works if you just plug and chug.
Vf=Vo + at

-5 = 5 + (a)(1)
a = -10

(So, if the velocity changes by 10 m/s^2 by 1 second, then it changes by 5 m/s^2 in .5 seconds. 5 - 5 = 0.)

Or you can use the information gathered above to form:

Vf = 5 + (-10)(.5)
Vf = 0


The reason you can do this is that once you have all but one variable in these equations, you can solve for the missing variable.

To speak to the issue regarding modifying time, as long as you adjust your other variables correctly, you will be fine. (As an example, we had to change Vf from -5 to X in the second equation because we no longer knew what the Vf was. We still knew Vo, A, and T, however.)

 

[PhysMatMan]

Or just use symmetry to quickly determine that the speed must be 0 m/s halfway through the acceleration.

 

[SKaminski]

Or just use symmetry to quickly determine that the speed must be 0 m/s halfway through the acceleration.

Absolutely true. Although I would suggest that silverice should get the basics down before he starts making shortcuts, you are completely correct.

 

[silverice]

Thx for the input. I definitely need to get my basics down, I just started.

 

[SuccessIsMine]

Thank Skaminski for clarity, I also had issues with this question. Thanks for posting the question Silverice. Thank you all for your additions!