# Total Distance travelled by a particle

## Homework Statement

what is the total distance travelled from time 0 - 10

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

## 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

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

"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"

HallsofIvy
Homework Helper
"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.

Last edited by a moderator:
understood, the car example made it clear

thanks