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First, let's define acceleration.

Acceleration defines how the velocity changes, and remember that velocity is a vector.

Then V = 10 m/s and V' = -10m/s are clearly different, while the speed is the same, one describes motion in one direction and the other describes motion in the opposite direction.

Where speed is the absolute value of the velocity:

S = IVI = I10 m/sI = 10 m/s

S' = IV'I = I-10 m/sI = 10m/s

If you have positive velocity and positive acceleration, then your velocity increases (meaning that your speed increases)

if you have positive velocity and negative acceleration, then your velocity decreases (meaning that your speed decreases)

if you have negative velocity and positive acceleration, then your velocity increases (meaning that your speed decreases)

if you have negative velocity and negative acceleration, then your velocity decreases (meaning that your speed increases)

Now, if you are in a freeway with no traffic, your velocity may be larger than 30 m/s (here we assume that you move in the positive direction, then your velocity is positive)

Then you see the sign, and you know that you need to decrease your velocity, meaning that you need to have negative acceleration until your velocity is 30 m/s or lower.

Concluding, the acceleration will be opposite to the direction of the velocity.

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80