"Moves towards the left" means that the velocity is negative.
The velocity function is an up-opening parabola.
It is negative between its -intercepts.
The particle moves to the left on the interval: .
Let be the location of point . (b) the distance, in , travelled by the particle during the first 3 seconds.
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
In the first second, it has moved: . . . . 2 units to the left.
In the next two seconds, it has moved: . . . . 32 units to the right.
Therefore, in the first 3 seconds, it moves: . units.
We already know that it is a parabola, but we can plot some points. (c) Sketch the velocity-time graph of the motion of the particle for 0 to 3
. . . . I dropped the "c"
| o (3,40)
| o (2,14)
- - + - - o - - + - - + - -
| o (1/3,-8/3)