AP Calculus Unit 3.2 Definitions - Velocity and Other Rates of Change

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Displacement

object’s total change in position over a certain interval: s(b) - s(a)

Average Velocity

object’s displacement divided by total change of time: s(b) - s(a) / b-a

Instantaneous Velocity

derivative of position at a given time t: s’(t), represented by v(t)

Speed

absolute value of object’s velocity: |v(t)|

Acceleration

derivative of velocity or second derivative of position at a given time t: v’(t) or s’’(t), represented by a(t)

Average Acceleration

object’s change of velocity divided by total change of time: v(a) - v(b) / b-a

Revenue

total income made from a product: r(x)

Cost

total spent to make a product: c(x)

Profit

net gain from a product, valued at the difference in revenue and cost: p(x) = r(x) - c(x)

Marginal Cost

additional cost of producing one more of an item, valued at the derivative of the cost to make products before the additional product: c’(x-1)

Marginal Revenue

additional revenue from producing one more of an item, valued at the derivative of the revenue gained from products before the additional product: r’(x-1)

Marginal Profit

additional profit of producing one more of an item, valued at the derivative of the profit gained from products before the additional product: p’(x-1)