Acceleration and deceleration in speed-time graphs

Question

What is the difference between 'the rate of deceleration' and 'deceleration'? Can deceleration have a positive gradient?

Answer 1

You have displacement, which when differentiated with respect to time, gives you velocity.

Velocity, when differentiated with respect to time, gives you acceleration.

Acceleration (or in this case, deceleration), when differentiated with respect to time, gives you something known as 'jerk'.

So:

Velocity = rate of change of displacement

Acceleration = rate of change of velocity

'Jerk' = rate of change of acceleration/deceleration

So if the deceleration has a positive gradient, you would have a positive 'jerk'.

See this post for more details: Jerk (physics)

Answer 2

These are two different things. First of all lets define rate. Rate means how much something is changing with time.

So Decelaeration or acceleration is defined by the formula

Change in velocity/Time

which means decelaration means how the speed is changing relative to time or rate of change of velocity.

So by definition rate of deceleration would mean rate of change of deceleration or change in deceleration with time which would be the gradient of an acceleration time graph.