# Integration, where am i going wrong here?

1. Nov 7, 2008

### devanlevin

given,-

$$\vec{a}$$$$_{x}$$=6t$$^{2}$$
$$\vec{a}$$$$_{y}$$=-4

vector V(t=0)=0
Vector R(t=0)=0

1-the displacement from the 1st to the 3rd second
2-the distance travelled fron the 2st to 3rd second
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using integration,
Vx=$$\int$$(ax)dt=2t$$^{3}$$
Vy=$$\int$$(ay)dt=-4t

x=$$\int$$(Vx)dt=0.5t$$^{4}$$
y=$$\int$$(Vy)dt=-2t$$^{2}$$

then i found r(t=1)=(0.5,-4)
and r(t=3)=(40.5,-18)

delta(r)=42.38, which is the answer to question 1
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now to find the distance travelled what i would like to do is integrate the vector V from 1 to 3, but once i get an answer for x and y, how do i connect them to get the scalar D, the distance he travelled?

Last edited by a moderator: Nov 7, 2008
2. Nov 7, 2008

### devanlevin

can i apply pythagarus with x and y values?

Last edited by a moderator: Nov 7, 2008
3. Nov 7, 2008

### physics girl phd

That sounds right... the motion here is separable along x- and y-directions.

4. Nov 8, 2008

### devanlevin

then i found r(t=1)=(0.5,-2)
and r(t=3)=(40.5,-18)

delta(r)=43.08, which is the answer to question 1,
i did this by adding the sqared values of x and y and then square root on the answer, i think this gives me the displacement

Last edited by a moderator: Nov 8, 2008
5. Nov 8, 2008

### devanlevin

thats fine, but what im looking for is the total distance travelled, not the displacemetn,,, so for example, if he travelled 10m X+, 7m X-, 20mY+,10mY-, what im looking for is 10+7+20+10, the total travelled, not sqrt(3^2+10^2),, problem here is its a complicated curve not straightforward, x then y. how do i calculate that? wont the integral just give me the displacement? also, how do i get a single scalar value, if i know that he walked 40m on X and 16 on y is the distance travelled43.08m?/ how else can i find it other thn pythagarus