Displacement, Velocity, and Acceleration
Three quantities, stacked. Displacement is how your position changed. Velocity is the rate at which position is changing. Acceleration is the rate at which velocity is changing. The math is the same operation at every level: subtract two values, divide by the elapsed time. The signs come along for the ride.
Velocity and acceleration look the same on the page. Both are signed numbers with arrows, both have the same operation behind them. But they answer different questions. A puck can move right while accelerating left. It can be momentarily at rest with a nonzero acceleration. Speeding up doesn't mean positive acceleration; it means velocity and acceleration point the same way, whichever direction that is.
The work
3 ways in · any order
Lesson
Displacement, Velocity, and Acceleration
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Position, velocity, and acceleration each measure change in the one before. The lesson works the d-v-a stack from the bottom up, then closes with a ten-scenario applet that drills the rate-of-rate move and the sign of acceleration when an object is slowing down.
Diagnostic
10-item topic check
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Ten items mapped to the displacement-velocity-acceleration stack. The hottest target is the velocity-vs-acceleration confusion that mistakes deceleration for negative acceleration; the rest probe sign discipline across the stack. Take it cold to surface what's still shaky, or after the lesson to confirm the fix held.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the misconception and you move on.