Practice question · Sort into groups
Sort each physical quantity by whether it is obtained by differentiating or by integrating.
Groups: Obtained by differentiating · Obtained by integrating
- Acceleration from velocity
- Position from velocity
- Total energy delivered by a push that changes as you go
- Velocity from position
Hints
- Differentiation extracts a rate; integration accumulates a total.
- Anything described as a 'total' or an 'accumulation over a path' is an integral.
Show the answer
Obtained by differentiating: Velocity from position, Acceleration from velocity
Obtained by integrating: Total energy delivered by a push that changes as you go, Position from velocity
Why
Rates come from derivatives and totals come from integrals, and the two are inverse, which is exactly the Fundamental Theorem of Calculus doing physical work. Items d1 and d4 are the same pair read in opposite directions.
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