Total Distance travelled by a particle

  • Thread starter phat2107
  • Start date
  • #1
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Homework Statement


what is the total distance travelled from time 0 - 10

the equations is 2t^3-15t^2+24t


Homework Equations





The Attempt at a Solution


time 0 it is at 0
time 10 its at 740

the answer is not 740

i have no idea how to solve this equation, no clue as to what im supposed to do

any help will be great

thanks
 

Answers and Replies

  • #2
Does the equation given describe the path of the particle?... or does it describe something else?
 
  • #3
11
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"A particle moves along a straight line and its position at time t is given by s(t)= 2t^3 - 15 t^2 + 24 t"
 
  • #4
HallsofIvy
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"A particle moves along a straight line and its position at time t is given by s(t)= 2t^3 - 15 t^2 + 24 t"

So s'(t)= 6t^2- 30t+ 24= 6(t^2- 5t+ 4)= 6(t- 4)(t- 1). For t between 0 and 1, s'(t) is positive (both t-1 and t- 4 are negative) so the particle is moving to the right. Between t= 1 and t= 4, s'(t) is negative (t- 4 is still negative but t- 1 is now positive) so the particle is moving to the left. Between t= 4 and t= 10, s'(t) is positive (t- 4 and t- 1 are now both positive) so the particle is moving to the right. The "total distance" traveled is the distance traveled between t= 0 and 1 plus the positive distance traveled between t= 1 and t= 4 plust the positive distance traveled between t= 4 and t= 10.p

it's like going 20 miles to the east, then 10 miles back to west, the 30 miles to the east again.
You are only 20- 10+ 30= 40 miles from your starting point but your speedometer will say that you have gone 20+ 10+ 30= 60 miles.
 
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  • #5
11
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understood, the car example made it clear

thanks
 

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