2.6 Calculate the average velocity of the car in different time interval

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Discussion Overview

The discussion revolves around calculating the average velocity of a car using a given position function over specified time intervals. Participants are working through a physics homework problem that involves mathematical reasoning and application of kinematic equations.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant shares a position function, $x(t) = at^2 - bt^3$, and expresses uncertainty about the polynomial representation.
  • Another participant reiterates the formula for average velocity, $\bar{v} = \dfrac{\Delta x}{\Delta t} = \dfrac{x(t_2)-x(t_1)}{t_2-t_1}$, and emphasizes that the units should be in $m/s$.
  • A participant provides a specific example using the function $x(t) = 1.50(t)^2 - 0.50(t)^3$ and calculates the average velocity for the interval from $t_1 = 0$ to $t_2 = 2$, arriving at a value of $2 \, m/s$.
  • Another participant repeats the calculation but arrives at a different conclusion, stating that the average velocity is $1 \, m/s$ instead.

Areas of Agreement / Disagreement

There is disagreement regarding the calculation of average velocity, with one participant asserting a value of $2 \, m/s$ and another claiming it is $1 \, m/s$. The discussion remains unresolved as both calculations are presented without consensus.

Contextual Notes

Participants have not clarified the values of constants $a$ and $b$ in the position function, which may affect the calculations. Additionally, there is a lack of consensus on the correct interpretation of the results.

karush
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OK I just had time to post and hopefully ok but still typos maybe
the graph was done in Deimos wanted to try tikx but not sure about the polynomial

trying to as many physics homework before classes start on Aug 26

Mahalo
 

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$x(t) = at^2-bt^3$

$\bar{v} = \dfrac{\Delta x}{\Delta t} = \dfrac{x(t_2)-x(t_1)}{t_2-t_1}$

units will be in $m/s$, not $m/s^2$ ... try again
 
skeeter said:
$x(t) = at^2-bt^3$

$\bar{v} = \dfrac{\Delta x}{\Delta t} = \dfrac{x(t_2)-x(t_1)}{t_2-t_1}$

units will be in $m/s$, not $m/s^2$ ... try again
$x(t)=1.50(t)^2-0.50(t)^3$

$\bar{v} = \dfrac{\Delta x}{\Delta t} = \dfrac{x(t_2)-x(t_1)}{t_2-t_1}$
so if $t_2=2$ and $t_1=0$ then

$\bar{v}=\dfrac{x(2)-x(0)}{2-0}=\dfrac{1.50(2)^2-0.50(2)^3-0}{2}=\dfrac{6-4}{2}=2\, m/s$
 
Last edited:
karush said:
$x(t)=1.50(t)^2-0.50(t)^3$

$\bar{v} = \dfrac{\Delta x}{\Delta t} = \dfrac{x(t_2)-x(t_1)}{t_2-t_1}$
so if $t_2=2$ and $t_1=0$ then

$\bar{v}=\dfrac{x(2)-x(0)}{2-0}=\dfrac{1.50(2)^2-0.50(2)^3-0}{2}=\dfrac{6-4}{2}=2\, m/s$
$\dfrac{6-4}{2} = \dfrac{2}{2} = 1 \, m/s$
 

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