Example 1a and 1b, pg. 25 Physics and Math Content Review

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jrashaad
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Example 1a and 1b, pg. 25 Physics and Math Content Review

Postby jrashaad » Sun Oct 29, 2017 6:03 pm

Please explain...

"Example 1a: Take north to be positive. A car is traveling south and speeding up. What is the sign of the acceleration?

Solution: Since the velocity vector points south and the car is speeding up, the acceleration vector must point south. With this sign convention, acceleration is negative.

Example 1b: Take north to be positive. A car traveling south speeds up from 10 m/s to 15 m/s in 10 s. What is its acceleration?

Solution: We write

a= -15 m/s - (-10 m/s)/10s = 0.5 m/s^2

This confirms our thinking in Example 1a."

To which I am confused. How can this "confirm our thinking in Example 1a" when the solution in 1a indicates that, by sign convention, acceleration is negative. Yet, the solution in 1b indicates that the acceleration is a positive 0.5 m/s^2. -15-(-10)/10 equals -0.5 not 0.5.
NS_Tutor_Andrew
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Re: Example 1a and 1b, pg. 25 Physics and Math Content Review

Postby NS_Tutor_Andrew » Sun Oct 29, 2017 10:29 pm

Hi jrashaad,

Thanks for checking in w/ the questions. First, a quick conceptual point -- "south" is being defined as negative by convention in this example, not acceleration.

More to the point, though, double check your signs. Let's work through the numerator first, ignoring units: -15-(-10) = -15+10 = -5. Then, combining that with the denominator, -5/10 = -0.5, so I think the sign usage in the example is correct.

Why it says "confirms our thinking in Example 1a" is just because in Example 1a we concluded that acceleration would be negative in this example, and in 1b we actually calculated it.

Hope this helps & please feel free to follow-up!
Andrew D.
Content Manager, Next Step Test Prep.

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