Question 1113960
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In my view, you incorrectly use terms/terminology.

The correct formulation is THIS:


<pre>
The velocity of a particle is given by the equation V = 3tē + 7t where V is measured in m/min.  
Find the displacement of the particle at t = 3 min if the initial {{{highlight(cross(displacement))}}} <U>position</U> is 5 m.
</pre>

You may think that the difference is insignificant. &nbsp;Yes, &nbsp;it is still not fatal, &nbsp;but it displays unprofessional using terminology &nbsp;(which is not good).


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;OK, &nbsp;now let's solve the problem !



<pre>
Since the velocity is given as a function of time t, the position is the integral of velocity over time.


The integral of  (3t^2 + 7t)dt  is equal to   {{{t^3 + (7/2)*t^2 + C}}},  where  C  is the constant.  The value of C is determined from the condition

that the initial position  (at t= 0)  is  5:  C = 5    (<<<---=== given !)


So, the final formula for the position is  P(t) = {{{t^3 + (7/2)*t^2 + 5}}} meters.


The position at t= 2 min is  P(3) = {{{3^3 + (7/2)*3^2 + 5}}} = 63.5 meters.


The displacement from the initial position is  63.5-5 = 58.5 meters.


<U>Answer</U>.  The displacement from the initial position is  58.5 meters.
</pre>

Solved.



I just solved today similar (TWIN) problem.


I think these two solved problems are enough for you, and you will not submit the TWIN problems more.