Calculus Derivatives Quiz

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Questions and Answers

What is the derivative of Q with respect to time t?

t extbf{i} + 3 extbf{j} + 2 extbf{k}
5t^2 extbf{i} + 5 extbf{j} - 5 extbf{k}
3t^2 extbf{i} + 2t extbf{j} + 3 extbf{k}
2t extbf{i} + extbf{j} + 3 extbf{k} (correct)

What is the value of the derivative of R with respect to time t?

5 extbf{i} + 1 extbf{j} + 5 extbf{k}
2t extbf{i} + extbf{j} + 5 extbf{k}
2t extbf{i} + extbf{j} - 1 extbf{k} (correct)
5 extbf{i} + extbf{j} - 5 extbf{k}

Which component of the expression for Q is the highest degree term?

3t extbf{k}
t extbf{j}
2t extbf{i}
t^{2} extbf{i} (correct)

Which of the following represents the combined derivatives of Q and R?

<p>$rac{dQ}{dt} + rac{dR}{dt} = (2t + 5) extbf{i} + (2t + 1) extbf{j} + (3 - 5) extbf{k}$ (A)</p> Signup and view all the answers

What is the value of the constant term in the expression for R?

<p>-3 (C)</p> Signup and view all the answers

Flashcards

Derivative of a Vector

The rate of change of a vector quantity with respect to time. It represents the direction and rate of change of motion of an object.

Component-wise Differentiation

The process of finding the derivative of a vector function, which is obtained by taking the derivative of each component of the vector function separately.

dQ/dt

A mathematical notation used to represent the derivative of a function. It is read as 'dQ/dt' and denotes the rate of change of Q with respect to the variable t.

Unit Vector

A unit vector that represents the direction of motion of an object. It is determined by dividing the velocity vector of the object by its magnitude.

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ω dQ/dt x dR/dt

The product of the derivative of the vector Q with respect to time, and the derivative of the vector R with respect to time, multiplied by the angular velocity ω.

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