Derivative Word Problem | Mathematics | Page 1

woven gazelle Feb 2, 2024, 5:39 PM

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Hello, I'm very confused on how to start this problem. Realistically, I have no idea what they want. Can I get some guidance on how to start it?

Screenshot_2024-02-02_at_10.38.06_AM.png

unkempt furnaceBOT Feb 2, 2024, 5:39 PM

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teal forge Feb 2, 2024, 5:52 PM

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the table has two rows: F and t
F shows the distance travelled by the horse in furlong (1 furlong = 220 yards = 0.125 miles)
t shows time passed since the horse started the race in seconds (1 second = 1/3600 hr)
the second column has F=1, t=21.1
so it travelled 0.125 miles in 211/36000 hr
=> the speed is distance/time = approx 21.33 miles per hour

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continue this for each of the furlongposts

woven gazelle Feb 2, 2024, 5:52 PM

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That would be part a, right?

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so there's technically 10 answers for a? hahaha

teal forge Feb 2, 2024, 5:53 PM

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the a part would we a textual description

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the 10 parter is b's answer

woven gazelle Feb 2, 2024, 5:54 PM

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I see, then at c what shall I do?

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I presume d is just looking at the b and c answers and figuring it out lol

teal forge Feb 2, 2024, 5:57 PM

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for acceleration it should be (current velocity - previous velocity)/(current time in seconds - previous time in seconds)
since acceleration is the rate of change of velocity

woven gazelle Feb 2, 2024, 6:03 PM

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Got it, thank you so so much!

teal forge Feb 2, 2024, 6:05 PM

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you should get close to 0 for acceleration since all the velocities are about the same i.e almost uniform motion

woven gazelle Feb 4, 2024, 7:25 AM

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teal forge the table has two rows: F and t F shows the distance travelled by the horse in f...

Sorry, how did you get 21.33 mph?

teal forge Feb 4, 2024, 8:06 AM

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woven gazelle Sorry, how did you get 21.33 mph?

1 furlong = 220 yards
220 yards = 0.125 miles
21.1 seconds = 21.1/3600 hr
So velocity is 0.125/(21.1/3600) mph

woven gazelle Feb 4, 2024, 8:16 AM

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ahhh, i was doing 0.125 * stuff

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thank you!

woven gazelle Feb 4, 2024, 10:28 PM

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teal forge 1 furlong = 220 yards 220 yards = 0.125 miles 21.1 seconds = 21.1/3600 hr So ve...

To find the mph at furlong post 2, would I do 0.25/(32.9/3600) mph which would give me 27.36 mph

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These are the answers I got

prime gateBOT Feb 4, 2024, 10:38 PM

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Someone

woven gazelle Feb 5, 2024, 1:09 AM

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teal forge for acceleration it should be (current velocity - previous velocity)/(current ti...

I personally don't think this is right?

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at furlong post 5, the acceleration is negative?

worldly flint Feb 5, 2024, 1:20 AM

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Yup. that means the velocity is decreasing

woven gazelle Feb 5, 2024, 1:22 AM

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worldly flint Yup. that means the velocity is decreasing

So that is the right equation? For example, finding the velocity at furlong post 2, it would be:

(27.36-21.33)/(32.9-21.1) = 0.51

worldly flint Feb 5, 2024, 1:23 AM

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Looks right

woven gazelle Feb 5, 2024, 1:24 AM

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amazing, thank you so much!

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I'll do this really quick to all 10

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I presume I just use 0 and 0 for the first furlong post?

worldly flint Feb 5, 2024, 1:24 AM

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Yup

prime gateBOT Feb 5, 2024, 2:13 AM

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Someone

woven gazelle Feb 5, 2024, 2:13 AM

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There's my data

prime gateBOT Feb 5, 2024, 2:15 AM

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Someone

woven gazelle Feb 5, 2024, 2:15 AM

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How's this for D?

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prime gateBOT Feb 5, 2024, 2:16 AM

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Someone
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

woven gazelle Feb 5, 2024, 2:16 AM

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How does like look, @worldly flint?

worldly flint Feb 5, 2024, 2:18 AM

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What are the units of acceleration in the table?

woven gazelle Feb 5, 2024, 2:19 AM

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I would think MPH?

worldly flint Feb 5, 2024, 2:20 AM

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That's velocity

woven gazelle Feb 5, 2024, 2:20 AM

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oh? then i have no idea hahaha

worldly flint Feb 5, 2024, 2:22 AM

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You can look at the question again for a hint

woven gazelle Feb 5, 2024, 2:24 AM

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oh

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miles per hour per second?

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MPHPS hahaha

prime gateBOT Feb 5, 2024, 2:24 AM

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Someone

woven gazelle Feb 5, 2024, 2:24 AM

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so I should use this?

worldly flint Feb 5, 2024, 2:26 AM

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mph/s

woven gazelle Feb 5, 2024, 2:32 AM

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Got it, thank you so so much!

woven gazelle Feb 5, 2024, 3:30 AM

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.solved

#Derivative Word Problem