EDIT: Ugh... I meant "calculating", of course.(adsbygoogle = window.adsbygoogle || []).push({});

This is an assignment that was due on the 16th. It's already been handed in, I just need some help with a question that I obviously was not able to answer in due time. I am coming back from a long, long hiatus from my academic pursuits and so some concepts that I had a firm grasp on in the past are now pretty fuzzy to me.

1. The problem statement, all variables and given/known data

P1. The position of a pinewood derby car was observed at various times; the results are summarized in the following table. Find the Average velocity of the car for (a) the first second, (b) the last 3s and (c) the entire period of observation.

t(s) 0-------1.0-------2.0-------3.0-------4.0-------5.0

x(m) 0-------2.3-------9.2-------20.7-------36.8-------57.5

P2. (a) Use the data in P1 to construct a smooth graph of position versus time.(b) By constructing tangents to the x(t) curve, find the instantaneous velocity of the car at several instants.(c) Plot the velocity versus time and, from this, determine the average acceleration of the car. (d) What was the initial velocity of the car?

2. Relevant equations

Average velocity: dx/dt

So P1 was easy enough:

(a) 2.30 m/s

(b) (57.5 - 9.20) / 3.00 = 16.1 m/s

(c) (57.5 - 0) / 5.00 = 11.5 m/s

P2:

(a) Constructing the graph was simple

(b) This is where I got stuck

(c) Couldn't calculate dv/dt because the previous part was incomplete

3. The attempt at a solution

So I know the instantaneous velocity corresponds to the limit of dx/dt as dt approaches zero, but I just didn't know how to go about doing that. The problem asks me to draw tangents and I did, I just didn't know how to derive the slope from that. I know the way to do this is pretty simple, but I'm just not getting it even after reading the relevant chapter several times.

Thanks in advance.

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# Calculting the slope of the tangent to find Instantaneous velocity

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