Solve Kinematics Problem: Find Distance Traveled Till t=5

[babita]

Homework Statement

Displacement of a particle moving in a straight line is
s= 6 + 12t - 2t^2
find the distance traveled till t=5.

Homework Equations

firstly i am having confusion in correctly interpreting the equation. The equation gives us the displacement in 't' th second.(correct?)
if i put t=0 in the eq i get s=0...now what does that mean? the particle is at x=6 at t=0?

at t=6.5 s=0 and before that s always comes out to be positive
as the particle is moving in straight line we can just add up the displacements till t=5 to get distance covered till t=5

The Attempt at a Solution

but how to add up displacments. the equation gives the displacement in t th sec.
like if i put t=5 in the equation i get s=16 but this is the displacement in 5th second only..i need the displacements in all time b/w 0 to 5 seconds
.
.
i also referred to the solution provided in the book which goes as follows:
ds/dt = v= 12-4t
( now i don't agree ds/dt would be the velocity...please explain)

 

[gneill]

I suspect that by "displacement" they mean "distance from the origin". Then the equation

s= 6 + 12t - 2t^2

would in fact be the position of the particle with respect to time, and ds/dt would indeed be its velocity.

 

[babita]

assuming that the answer comes correct...thanks...but i want to kill the author...it discourages if one can't solve a prob even after studying deeply :((