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AP Calculus BC 9.4: Vector-Valued Derivatives

Practise AP Calculus BC 9.4 by differentiating vector-valued position components and evaluating the resulting velocity vector at a specified time.

Syllabus
Effective Fall 2020
Course
AP Calculus BC

Exam points

  • Differentiate x(t) and y(t) componentwise, then evaluate the velocity vector at a given time.

CHA-3.H—Calculate derivatives of vector-valued functions question 1

[Maximum number: 1]

For time t>0, the position of a particle moving in the x y-plane is given by the vector ⟨1t,e3t⟩\left\langle\frac{1}{t}, e^{3 t}\right\rangle. What is the velocity vector of the particle at time t=2 ?

A

⟨12,e6⟩\left\langle\frac{1}{2}, e^{6}\right\rangle

B

⟨14,e6⟩\left\langle\frac{1}{4}, e^{6}\right\rangle

C

⟨14,3e6⟩\left\langle\frac{1}{4}, 3 e^{6}\right\rangle

D

⟨−14,e6⟩\left\langle-\frac{1}{4}, e^{6}\right\rangle

E

⟨−14,3e6⟩\left\langle-\frac{1}{4}, 3 e^{6}\right\rangle

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