# How can there be negative acceleration when the object’s velocity is increasing?

If the velocity of the object changes from -2m/s to -6m/s, then its velocity has increased and therefore the acceleration must be positive. But using the formula for acceleration (or while plotting it on the graph) the acceleration comes as negative.

$$\frac {\Delta v}{\Delta t} = \frac {-4m}{s^2}$$ Since the acceleration value is negative, (I am assuming) this means that the velocity is decreasing. But how?

• What is the meaning of a -2m/s speed for you? What is a car that goes at -2m/s? If you're talking about the magnitude of the velocity, it should never be negative. If you're talking about a vector described in a cartesian set of axis, you just have to write it a bit more carefully, and you will see there is no contradiction between the direction of the vector acceleration and the evolution of your speed vector Commented Jul 1, 2021 at 8:02
• Positive or negative acceleration generally means opposite accelerations in the same axis. Commented Jul 1, 2021 at 8:14

## 2 Answers

The sign of acceleration is the direction of the acceleration. If positive the acceleration is in the positive direction. If negative then the acceleration is in the negative direction. There are 4 cases:

1. If the object is moving in the positive direction has a negative acceleration it is slowing down.
2. Likewise if an object is moving in the negative direction and has a positive accelrration it is slowing down.
3. If the object is moving in the positive direction with a positive acceleration it is speeding up.
4. Likewise if an object is moving in the negative direction with a negative acceleration it is speeding up.
• in other words both velocity and acceleration are vectors Commented Jul 1, 2021 at 10:27

Actually, the velocity is decreasing: -6m/s is less than -2m/s.

Consider changing frame of reference: Imagine an inertial system (frame of reference) moving with -6m/s. Relative to it, the object moves in the beginning with (-2 - (-6)) m/s = 4m/s. At the end it moves with (-6 - (-6)) m/s = 0m/s. So its movement stopped, the velocity decreased and its acceleration was (correctly) negative.

When you say "its velocity has increased", you are speaking of absolute values. Then the calculation would go (|-6| - |-2|)m/s = 4m/s, and the resulting acceleration is positive as you would expect.