Hello, nikk!
"Moves towards the left" means that the velocity is negative.
The velocity function is an upopening parabola.
It is negative between its intercepts.
intercepts: .
The particle moves to the left on the interval: .
(b) the distance, in , travelled by the particle during the first 3 seconds. Let be the location of point .
This is the position of the particle when
The position function is given by: .
We have: .
The particle stops and changes directions when
In (a), we found that this happens at: . and
At
At
In the first second, it has moved: . . . . 2 units to the left.
At
In the next two seconds, it has moved: . . . . 32 units to the right.
Therefore, in the first 3 seconds, it moves: . units.
(c) Sketch the velocitytime graph of the motion of the particle for 0 to 3 We already know that it is a parabola, but we can plot some points.
. . . . I dropped the "c"
Code:

 o (3,40)




 o (2,14)


  +   o   +   +  
 (1,0)
(0,2)o
 o (1/3,8/3)
