We notice sudden changes in anything. We don't notice gradual change, whether in time or spread over space. If the car is moving uniformly along straight flat road, its acceleration a=0. Its velocity v is constant.
When the brake pedal is pushed, friction causes the car to decelarate. a = some negative number. You can't avoid that. You want to stop? Your velocity must decrease. (Duh.)
What the passengers feel is the change from a=0 to a=-5.6948 m/s^2 (making up a number.) You want that change to be gradual. Before braking, when a=0, and assuming you're sufficiently skilled and anticipate needing to stop, you light apply brakes. Suppose you make a linearly decrease from 0 to -5.6948, and once there, keep it there. This linear decrease takes place over, let us say, 5 seconds. Likewise, a linear let-up to a=0 timed perfectly as the car comes to a stop.
Remember acceleration is the time derivative of velocity. Velocity, therefore, is the indefinite integral of acceleration, which is a piecewise linear function of time. Plotting velocity vs time, you'd see pieces of parabolas joined together.
Now, I wonder if passengers would feel the change in acceleration during that time it's changing? It's changing gradually, but it is going from non-changing (zero) to changing linearly, to finally not changing (steady strong braking), with no sudden jumps. Maybe the game is to soften the rate of change of acceleration, to not suddenly go from flat to linear. Look at the time derivative of acceleration - it's all step functions in our example!
So make the time derivative of acceleration be piecewise linear, no jumps. Then the acceleration is smooth, no sudden changes in slope where parabolas join. Velocity is very smooth, described by 3rd degree polynomials. A good driver/pilot approaches this kind of smoothness by intuitive feel and experience.
The speedometer on an airplane measures air speed, that is speed relative to a big block of air, not ground speed.
So if it is traveling at an air speed of 60 miles per hour, that means if there were two balloons 60 miles apart, it could travel between them in one hour.
However, if in that hour, the entire block of air moved 10 miles the other way, then at the end of the hour, the plane would still have covered 60 miles of air, but only 50 miles of ground.
The speedometer on an automobile measures ground speed, that is speed relative to the ground, not air speed.
So if the car is doing 60 miles per hour, that means after one hour, it will have traveled 60 miles measured on the ground.
Regardless of the wind.
Best Answer
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.