# Thread: Rectilinear Motion using Integration: Find displacement & distance traveled on time

1. ## Rectilinear Motion using Integration: Find displacement & distance traveled on time

A particle moves with a velocity of v(t)= m/s along an s-axis. Find the displacement and the distance traveled by the particle in a given time interval.

11) v(t) = t^3 - 3t^2 +2t 0 < t <3

I did sigma(t^3-3t^2 + 2t)dt

I got 1/4t^4 + 3/3t^3 + 2/2 t^2 and evaluated on 0-3

(81/4 - 108/4 + 36/4)

The answer is supposed to be 9/4 m.... Where did I go wrong ??? I've redone this problem like 6 times

2. ## Re: Rectilinear Motion using Integration: Find displacement & distance traveled on ti

First, in the velocity equation you have a -3t^2 but when you integrate you have a positive.
But your expression below is correct:

81/4-108/4+36/4=(117-108)/4=9/4.

I don't think you have done anything wrong. Also, if you want to find the distance you need to take into account when the velocity is negative. If you look carefully (i.e. differentiate) the velocity expression, you will see that is positive on some intervals but negative on others. When you integrate to find the speed you need to consider this.

3. ## Re: Rectilinear Motion using Integration: Find displacement & distance traveled on ti

Thank you so much ... I can't believe I made such a dumb mistake

4. ## Re: Rectilinear Motion using Integration: Find displacement & distance traveled on ti

You are welcome. Hey, there is no dumb mistake.

"Only those who never try anything new don't make mistakes."
- A. Einstein