TITLE: If I am decelarating forwards am I accelerating backwards?
QUESTION [1 upvotes]: If I am in a car and I put the brakes on so that I am slowing down (decelerating) am I then accelerating backwards? e.g. If I am decelerating in this car at -5ms⁻² am I accelerating backwards at 5ms⁻² ?

REPLY [0 votes]: I am slowing down (decelerating) am I then accelerating backwards?  

The implication here is that the direction of the acceleration is in the opposite direction to the velocity.
I think that you should avoid the word decelerate as it can be taken to mean a reduction in the speed of the car but this might not always be so.  
Suppose a car is moving at $\rm 10 \, m\,s^{-1}$ up a hill and suddenly the engine stops working and the brakes are not applied.  
The car then decelerates down the hill at $\rm 2 \,m\,s^{-2}$ ie it has an acceleration of $\rm -2 \,m\,s^{-2}$ up the hill.
So after $1\,\rm s$ the velocity of the car is $\rm 8 \, m\,s^{-1}$ up the hill and after $5\,\rm s$ the car is at rest.
All fine so far as the speed of the car has decreased from  $\rm 10 \, m\,s^{-1}$ to be at rest.  
However what happens after $6\, \rm s$?
The velocity of the car is $\rm 2 \, m\,s^{-1}$ down the hill ie the speed of the car is now increasing.  

If I am decelerating in this car at -5ms⁻² am I accelerating backwards at 5ms⁻² ?  

Let the car be moving in the positive x-direction.
A deceleration implies that the acceleration is in the negative x-direction.
A negative deceleration implies that the acceleration is in the positive x-direction.  
With the car moving in the positive x-direction a deceleration of 5ms⁻² implies that the car has an acceleration of 5ms⁻² in the negative x-direction.  
With the car moving in the positive x-direction, a deceleration of -5ms⁻² implies that the car has an acceleration of +5ms⁻² in the positive x-direction.
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