I'm a TA and there is an inconsistency in what the solutions manual states and what the students are turning in, but both seem correct.(adsbygoogle = window.adsbygoogle || []).push({});

The Latex code isn't working properly for the post, but it is easy to see what equations are used

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

A particle of mass m moves along the x axis. Its position varies with time according to [tex]$x$=2t^3 - 4t^2[/tex] , where x is in meters and t is in seconds. Find

a. The velocity and acceleration of the particle as functions of t.

b. The power delivered to the particle as a function of t

c. the work done by the net force from [tex]t=0 $to$ t=t_{1}[/tex]

2. Relevant equations

The first 2 parts are easy and the answers are given by

[tex]$v$=6t^2 - 8t $;$ $a$=12t - 8 $;$ $P$=power=8mt(9t^2 - 18t + 8)[/tex]

3. The attempt at a solution

The problem is that both solutions are correct mathematically, but they are different. Therefor one must be wrong and I need someone to tell me which on, and WHY?

Solution manual

[tex]$w$=\int_0^t \! P \, dt

$w$=\int_0^t \! 8m(9t^3 - 18t^2 + 8t) \, dt

$w$=2mt^{2}(9t^2-24t+16)[/tex]

Student Solution

[tex]$w$=F\Delta x=ma\Delta x = m(12t - 8)(2t^3 - 4t^2)[/tex]

This becomes,

[tex]$w$=m(24t^4 - 64t^3 + 32t)[/tex]

Which one of these is wrong, since the math is right on both of them and the equations are valid for power?

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# TA need help grading HW question!

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