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Distance/displacement integration problem

  • Thread starter zachem62
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  • #1
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Homework Statement




Suppose that v(t)=t2 -2t -8, 1≤t≤6 is the velocity function (in meters per second) of a particle moving along a line. Find a) the displacement and b) the distance traveled by the particle during the given time interval.

Homework Equations





The Attempt at a Solution



so i integrated the velocity function at the interval 1 to 6 and got the answer (-10/3)m. so i have no idea if this is the distance or displacement and if it is one of those, then how would i find the other one?

thanks!

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Ray Vickson
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Homework Statement




Suppose that v(t)=t2 -2t -8, 1≤t≤6 is the velocity function (in meters per second) of a particle moving along a line. Find a) the displacement and b) the distance traveled by the particle during the given time interval.

Homework Equations





The Attempt at a Solution



so i integrated the velocity function at the interval 1 to 6 and got the answer (-10/3)m. so i have no idea if this is the distance or displacement and if it is one of those, then how would i find the other one?

thanks!

Homework Statement





Homework Equations





The Attempt at a Solution

Think about whether the particle can change its direction of travel between times 0 and 6, and if it can, think about what the integral ∫v(t): t=0..6 actually computes.

RGV
 
  • #3
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Think about whether the particle can change its direction of travel between times 0 and 6, and if it can, think about what the integral ∫v(t): t=0..6 actually computes.

RGV
in the question it says that t can only be between 1 and 6 so i can't use any 0. and it is possible that the particle can change direction and my guess is this means that the integral ∫v(t): t=1 to 6 computes the distance. am i right?

then how would i get displacement? can u give me a hint? i know that its the final position minus initial position but i don't know if i'm supposed to get it by integrating the function or do something else.
 
  • #5
HallsofIvy
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v(t)=t^2 -2t -8, 1≤t≤6
When t= 6, v(6)= 36- 12- 8= 16.
When t= 1, v(1)= 1- 2- 8= -11.
Now, what was the displacement? (Do you know what "displacement" means?)
 

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