Sign Convention

  • Displacement, velocity and acceleration are all vector quantities. They thus have both magnitude and direction.
  • Rectilinear motion refers to motion which occurs strictly along a straight line. Since only two directions are possible, a positive sign indicates one direction, and the negative indicates the opposite direction.
  • When velocity is negative
    1. “decreasing” velocity actually implies increasing speed.
    2. positive acceleration actually implies decreasing speed and vice versa.
  • For example, let’s adopt the “rightward is positive” convention for the motions below.

1 pospos

  • Since the sheep is moving rightward and speeding up, its velocity is represented by more and more positive numbers.
  • Since the velocity is increasing, the acceleration is positive.

1 pospos

  • Since the sheep is moving leftward and speeding up, its velocity is represented by more and more negative numbers.
  • Since the velocity is “decreasing”, the acceleration is negative.

1 pospos

  • Since the sheep is moving rightward but slowing down,  its velocity is represented by less and less positive numbers.
  • Since the velocity is decreasing, the acceleration is negative.

1 pospos

  • Since the sheep is moving leftward but slowing down,  its velocity is represented by less and less negative numbers.
  • Since the velocity is “increasing”, the acceleration is positive.

 

  • In a nutshell, the speed increases if the velocity and acceleration have the same sign, and decreases if the velocity and acceleration have opposite signs.

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