Three questions, three arrows

Stand on a road. Pick a start line and call it zero. Everything to the right is positive, everything to the left is negative. Now the first question, Where is it?, has a one-number answer: 12 m means twelve metres right of the line, −5 m means five to the left. That number is position. Move from one position to another and the change is your displacement: from 12 m to −5 m is a displacement of −17 m, seventeen metres leftward, no matter how wiggly the path was.

Second question: How fast, and which way? That is velocity. 4 m/s to the right and 4 m/s to the left are the same speed but different velocities, so we give them different signs: +4 and −4. On the road below, the blue arrow is the velocity. Longer arrow, faster car. Pointing left, negative number.

Third question, the one people skip: Is that changing? If the velocity is changing, the car is accelerating, whether it is speeding up, slowing down or turning. Acceleration is how much the velocity changes every second. An acceleration of 2 m/s² means the velocity grows by 2 m/s each second: 0, 2, 4, 6. The red arrow is acceleration. Here is the part that trips everyone: the red arrow can point the opposite way to the blue one. Then the car is slowing down.

Why three separate questions? Because they can disagree, and that is where all the interesting physics hides. A ball at the top of its throw has zero velocity but full acceleration. A car cruising at 120 km/h has huge velocity and zero acceleration. A satellite has steady speed and yet accelerates every second, because its direction keeps changing. Whenever you feel confused in this course, ask: which of the three questions am I actually being asked?