What is the Displacement of a Particle from t=1s to t=3s?

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To determine the displacement of a particle from t=1s to t=3s, the position vector is given as r=-(5,0m/s)t i + (10,0m/s^2)t^2 j + (7,0m -(2,0m/s^3)t^3) k. By substituting t=1 and t=3 into the equation, two position vectors are obtained: (-5,10,5) at t=1 and (-15,90,-20) at t=3. The displacement vector is found by subtracting the position vector at t=1 from that at t=3. The magnitude of the displacement can then be calculated using the Pythagorean theorem. This method effectively provides the particle's displacement over the specified time interval.
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Homework Statement



Determine the displacement of this particle from t=1s to t=3s

r=-(5,0m/s)t i + (10,0m/s^2)t^2 j + (7,0m -(2,0m/s^3)t^3) k


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The Attempt at a Solution


I don't have an idea how to do this if I should to it by replacing t by 1 and then getting the magnitude of the vector for example. or should i get the value of t = 1 by each component alone and substract the components of 3 - the components of 1 ?

I must finish this soon thanks for the help in advance
 
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the equation represents the position vector in the form of coordinates.make t=1and t=3,you will get two position vectors (-5,10,5)and(-15,90,-20).use the knowledge of vector of the form of coordinates and you will get the answer
 
azureth said:
the equation represents the position vector in the form of coordinates.make t=1and t=3,you will get two position vectors (-5,10,5)and(-15,90,-20).use the knowledge of vector of the form of coordinates and you will get the answer

Now I must only get the magntitude of the vectors? thanks
 
you may get the magnitude of the vector of displacement by using pythagorean theorem
 
azureth said:
you may get the magnitude of the vector of displacement by using pythagorean theorem

thanks a lot
 
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