According to Reisnick and Halliday, retardation is the acceleration in the negative direction of time axis ie. opposite to the motion. Decreasing accleretion is the decrease in the magnitude of time rate of change of velocity. Am I correct or not? What is the $v$-$t$ graph with retardation and decreasing acceleration? [I don't think they are same.]
[Physics] the difference between negative acceleration and decreasing acceleration
accelerationkinematics
Related Solutions
Hopefully this helps. As you can see, acceleration is a change in velocity. When you're decreasing acceleration, you're decreasing the change in velocity. When the acceleration hits zero, your velocity is constant.
The car situation might seem tricky because of wind resistance, friction, in real life your car will slow down once you take your foot off the gas pedal However, in a system without friction and wind resistance because of inertia, it would keep moving at the same velocity if a = 0 as seen above and increasing in speed when a > 0.
Best Answer
A simple example, particle moving in one dimension, say $x$:
A particle has a (negative) acceleration equal to $-2m/s^2$ (note it is constant acceleration, yet negative, i.e opposite to direction of motion or to direction of cummulant force applied to particle)
Another particle has a (decreasing) acceleration equal to $1/(kt)^2 m/s^2$ (note it is positive acceleration i.e in the same direction as direction of motion, yet decreasing in magnitude with time)
To sum up, negative or opposite acceleration refers to direction, while decreasing acceleration refers to magnitude.
The above are only illustrative examples, many more examples of negative and decreasing accelerations (or both).
Some mock v-t graphs for various types of acceleration: