(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The acceleration of a particle is given by a_{x}(t) = 2.90t - 2.06

Q. Find the initial velocity v_{0x}such that the particle will have the same x-coordinate at time t = 4.06 as it had at t = 0.

2. Relevant equations

v_{x}= v_{0x}+ [tex]\int[/tex]a_{x}dt evaluated from 0 to t.

x = x_{0}+ [tex]\int[/tex]v_{x}dt evaluated from 0 to t.

This is defined for straight-line motion with varying acceleration, which appears to fit my scenario.

3. The attempt at a solution

v_{x}= v_{0x}+ [tex]\int[/tex](2.90t - 2.06)dt evaluated from 0 to t.

v_{x}= v_{0x}+ 1.45t^{2}- 1.03t

x = x_{0}+ [tex]\int[/tex](v_{0x}+ 1.45t^{2}- 1.03t)dt evaluated from 0 to t.

x = x_{0}+ [tex]\int[/tex](1.45t^{2}- 1.03t)dt + v_{0x}[tex]\int[/tex]dt

x = x_{0}+ v_{0x}t + (1.45t^{3}/3) - (1.03t^{2}/2)

Unfortunately this is as far as I got. I don't understand how to incorporate the values I was given for t. Could someone point me in the right direction please?

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# Homework Help: Determining initial velocity and instant velocity

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