Motion Problem: Race Car's Position & Instantaneous Velocity at t = 3.5 s

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The discussion revolves around a motion problem involving a race car's position described by the equation x = (5.0 m/s)t + (0.80 m/s³)t³. Participants express confusion regarding part (b), which requires calculating the instantaneous velocity at t = 3.5 s using varying time intervals. The average velocity over the first 3.5 seconds is noted as 14.8 m/s, prompting a comparison with the instantaneous velocity results. The conversation emphasizes the importance of understanding the definitions of average and instantaneous velocity in solving the problem. Clarifying these concepts is essential for accurately completing the assignment.
Rymac
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This problem seems simple enough, I guess I just don't really understand what it's looking for in the (b) portion.
A race car moves such that its position fits the relationship where x is measured in meters and t in seconds.
x = (5.0 m/s)t + (0.80 m/s³)t³

(a) Plot a graph of the car's position versus time. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Determine the instantaneous velocity of the car at t = 3.5 s, using time intervals of 0.40 s, 0.20 s, and 0.10 s.

Δt = 0.40 s ____________m/s

Δt = 0.20 s ____________m/s

Δt = 0.10 s ____________m/s


(c) Compare the average velocity during the first 3.5 s with the results of (d).
The average velocity of _14.8_ m/s is (*d1*) much less than (d2) about the same as (d3) much greater than the instantaneous velocity.
 
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You need to show that you have but some kind of thought into this problem.

what is your definition of Average and instanenous velocity?
 

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