Apentix/AP Calculus AB/Unit 7: Differential Equations/Question

AP Calculus ABeasymcq1 pt

A vehicle moves in a straight line, and its acceleration is proportional to its velocity $v$ . Which differential equation describes the velocity?

A.

\dfrac{dv}{dt} = kv

B.

\dfrac{dv}{dt} = kt

C.

\dfrac{dv}{dt} = \dfrac{k}{v}

D.

\dfrac{dv}{dt} = k

Explanation

Core Concept

Acceleration is $\dfrac{dv}{dt}$ , so acceleration proportional to velocity gives $\dfrac{dv}{dt}=kv$ .

Correct Answer

A $\dfrac{dv}{dt} = kv$

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