# Total Distance travelled by a particle

1. Oct 12, 2009

### phat2107

1. The problem statement, all variables and given/known data
what is the total distance travelled from time 0 - 10

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

2. Relevant equations

3. The attempt at a solution
time 0 it is at 0
time 10 its at 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

2. Oct 12, 2009

### calimechengr

Does the equation given describe the path of the particle?... or does it describe something else?

3. Oct 12, 2009

### phat2107

"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. Oct 12, 2009

### HallsofIvy

Staff Emeritus
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.

Last edited: Oct 12, 2009
5. Oct 12, 2009

### phat2107

understood, the car example made it clear

thanks