# Positive and Negative Acceleration Scenarios

#### Back to Positive and Negative Acceleration

We've learned that it's not the acceleration sign that tells us whether an object has undergone positive or negative acceleration; instead we need to compare it to the objects' initial velocity [sign].

This is sometimes a little hard to get your head around, because in many scenarios it's true that the sign of the acceleration will be the same as the type of acceleration that the object has undergone. Let's take a look at a couple scenarios where this is NOT the case.

## Scenario 1

**Both initial and final velocities are negative.**

**Example: A car travelling in the southerly direction changes velocity from 4 m/s to 8 m/s over 2 seconds.**

*a) Calculate the acceleration required for this change in velocity.*

Acceleration = (velocity_{final} - velocity_{initial}) ÷ time

Acceleration = (-8 m/s - -4m/s) ÷ 2 s

Acceleration = -4 m/s ÷ 2 s

Acceleration = -2 m/s

** b) Determine if the car has undergone positive or negative acceleration.**.

If you were to base your answer to part b) on the sign associated with the acceleration in part a), then you'd say the car underwent negative acceleration.

**But this is INCORRECT**. The car is actually travelling at a faster speed AND in the same direction. It has undergone POSITIVE acceleration.

## Scenario 2

**The object starts travelling in the opposite direction.**

**Example: A car changes velocity from 4 m/s westerly to 4 m/s easterly over 2 seconds.**

*a) Calculate the acceleration required for this change in velocity.*

Acceleration = (velocity_{final} - velocity_{initial}) ÷ time

Acceleration = (4 m/s - -4m/s) ÷ 2 s

Acceleration = 8 m/s ÷ 2 s

Acceleration = 4 m/s

*b) Determine if the car has undergone positive or negative acceleration.*

If you were to base your answer to part b) on the sign associated with the acceleration in part a), then you'd say the car underwent positive acceleration. **But this is INCORRECT**. Why? *Because positive acceleration means that the car increased its velocity in the same direction as it was initially travelling in.* Although the car is travelling at a faster final

*speed*, it is moving in the opposite direction. This means that it must have undergone NEGATIVE acceleration.

## Other Scenarios

The table below describes every scenario possible in simple movement i.e. within the same plane (North-South, OR East-West). To download the document visit Slideshare here: