SOLUTION: 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 displacement is 5

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Question 1113960: 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 displacement is 5 m.
Round your answer to the nearest whole number.
Found 2 solutions by ikleyn, amalm06:
Answer by ikleyn(52866)   (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 = 3tē + 7t where V is measured in m/min.  
Find the displacement of the particle at t = 3 min if the initial  position is 5 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  (3t^2 + 7t)dt  is equal to   ,  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) =  meters.


The position at t= 2 min is  P(3) =  = 63.5 meters.


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


Answer.  The displacement from the initial position is  58.5 meters.

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.


Answer by amalm06(224)   (Show Source): You can put this solution on YOUR website!






=





Δs=s2-s1=63.5-5=58.5 m (Answer)
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