How to Find the Total Distance Traveled from 0 to 10 Seconds?

[jack911]

Homework Statement

the following is a equation to find the displacement of a particle. I've found it is instantaneous at rest at t=5. now need to find the distance traveled between 0 to 10s.

i found distance traveling between 0 to 5 s is 7.5

but no idea how to find distance traveled between 5 to 10s...please help.

Homework Equations

s=0.7t^2-0.1t^3+0.5t

The Attempt at a Solution

32.5m

 

[quantumdude]

You don't need to know when the velocity is zero to solve this, you need to know at what time $T$ the displacement is zero. Then the total distance traveled is $|s(T)-s(0)|+|s(10)-s(T)|$.

 

[jack911]

yes i use|s(5)-s(0)|+|s(10)-s(5)| = 7.5+32.5=40but the ans is 40 instead of 32.5

 

[quantumdude]

That's no good. The displacement isn't zero when t=5.

 

[jack911]

thanks i got the ans but i wonder why we have to know what time the displacement is zero??i can't get it~.~

 

[quantumdude]

You need to know when the displacement is zero because after that time the displacement becomes negative (and distance is never negative).

 

[jack911]

i get it but i wonder can i do it with find t when v=0? because your method seem not suitable for finding distance between t and t1(where t and t1 are the time when s=0)

can you please point out my mistake in the following equation?

|s(5)-s(0)|+|s(10)-s(5)| = 7.5+32.5=40

thanks a lot:)