SOLUTION: The velocity of a particle is given by the equation V = 6tē+ 2t where V is measured in m/min. Find the displacement of the particle at t = 2 min if the initial displacement is 9 m

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Question 1114038: The velocity of a particle is given by the equation V = 6tē+ 2t where V is measured in m/min. Find the displacement of the particle at t = 2 min if the initial displacement is 9 m
Answer by ikleyn(52885) About Me  (Show Source):
You can put this solution on YOUR website!
.
In my view, you incorrectly use terms/terminology.
The correct formulation is THIS: 

    The velocity of a particle is given by the equation V = 6tē+ 2t where V is measured in m/min.  

    Find the displacement of the particle at t = 2 min if the initial highlight%28cross%28displacement%29%29 position is 9 m

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

            OK,  now let's solve the problem ! 


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


The integral of  (6t^2 + 2t)dt  is equal to   2t^3 + 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  9:  C = 9    (<<<---=== given !)


So, the final formula for the position is  P(t) = 2t%5E3+%2B+t%5E2+%2B+9 meters.


The position at t= 2 min is  P(2) = 2%2A2%5E3+%2B+2%5E2+%2B+9 = 29 meters.


The displacement from the initial position is  29-9 = 20 meters.


Answer.  The displacement from the initial position is  20 meters.

Solved.