Practice question · Multiple choice
Position, velocity and acceleration are successive derivatives. Why does a car with zero velocity at the top of a hill not also have zero acceleration?
Hints
- Think of a ball at the top of its flight.
- Ask whether a quantity being zero constrains its rate of change.
Show the answer
C. Because zero velocity says nothing about how it is CHANGING
Why
A value and its rate of change are independent at an instant. This is the same reason a ball thrown upward has at the top of its arc even though it is momentarily at rest.
Practise Derivatives as local rate of change
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