# 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.

• 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.

• 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.

• 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.

• 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.