Question 1

Which of the following is the correct solution for $$x in $$the quadratic equation $$3x^2 - 5x - 2 = 0$?

Accepted Answer

$$x = \dfrac{5 \pm \sqrt{49}}{6}$$

Question 2

Given the function $$f(t) = 4t^2$ - 2t + 5$$, what is the average rate of change of $$f$$ from $$t = 1 to$$ $$t = 3$$?

Accepted Answer

$$13$$

Question 3

A vector $$\vec{V}$$ has magnitude $$V = 15.0$$ and direction $$	heta = 40.0^\circ$$ above the horizontal. What is the vertical component $$V_y$$?

Accepted Answer

$$V_y = 15.0 \sin(40.0^\circ)$$

Question 4

A right triangle has an adjacent side of length $$6.0$$ units and opposite side $$8.0$$ units. What is the length of the hypotenuse?

Accepted Answer

$$10.0$$ units

Question 5

Given $$	an(	heta) = 2$$ and $$	heta is in $$Quadrant I, what is $$\sin(	heta)$$?

Accepted Answer

Question 6

A unit circle is centered at the origin. What are the Cartesian coordinates of the point corresponding to $$	heta = 120^\circ$$?

Accepted Answer

$$(-\dfrac{1}{2}, \dfrac{\sqrt{3}}{2})$$

Question 7

Given the function $$x(t) = 3t^2$ + 2t$$, what is the acceleration $$a$$?

Accepted Answer

$$a = 6t$$

Question 8

Given the acceleration function $$a(t) = 3t^2$ + 2t$$, what is the first integral of $$a(t)$$ with respect to $$t$$?

Accepted Answer

$$v(t) = t^3$ + t^2$ + C$$

Question 9

Given a position vector as a function of time $$\vec{r}(t) = (3t^2$ \hat{i} + 2t \hat{j} + t \hat{k})$$, what is the velocity vector $$\vec{v}(t)$$?

Accepted Answer

$$\vec{v}(t) = (6t \hat{i} + 2 \hat{j} + \hat{k})$$

Question 10

A particle's velocity is given by $$\vec{v}(t) = (4t \hat{i} + 3 \hat{j}). $$What is the displacement vector $$\Delta \vec{r}$$ from $$t = 0 to$$ $$t = 2$$?

Accepted Answer

$$\Delta \vec{r} = (8 \hat{i} + 6 \hat{j})$$

Question 11

If $$f(x) = 4x^2$ - 2x + 5$$, what is $$f(2)$$?

Accepted Answer

$$17$$

Question 12

Given $$\sin^2$(	heta) + \cos^2$(	heta) = 1$$, which of the following is a correct application for $$	heta = 45^\circ$$?

Accepted Answer

$$\sin^2$(45^\circ) + \cos^2$(45^\circ) = 1$$

Question 13

If $$x = \dfrac{2a^2$ - 3}{a - 1}$$ for $$a 
eq 0, 1$$, what is $$x$$ when $$a = 2$$?

Accepted Answer

$$x = 5$$

Question 14

A vector $$\vec{V}$$ has magnitude $$V = 10$$ and direction $$	heta = 30^\circ$$ above the horizontal. What is the horizontal component $$V_x$$?

Accepted Answer

$$V_x = 10 \cos(30^\circ)$$

Question 15

Given the function $$x(t) = 3t^2$ + 2t$$, what is the velocity $$v at$$ $$t = 1$$?

Accepted Answer

$$v = 8$$

Question 16

If a function $$a(t) = 3t^2$ + 2t$$ represents acceleration, what physical quantity does the second integral of $$a(t)$$ with respect to $$t$$ represent?

Accepted Answer

Position

Question 17

Given a position vector $$\vec{r}(t) = (3t^2$ \hat{i} + 2t \hat{j} + t \hat{k})$$, what is the acceleration vector $$\vec{a}(t)$$?

Accepted Answer

$$\vec{a}(t) = (6 \hat{i})$$

Question 18

If $$	an(	heta) = 2$$ and $$	heta is in $$Quadrant I, what is $$\cos(	heta)$$?

Accepted Answer

$$\dfrac{1}{\sqrt{5}}$$

Question 19

A right triangle has an adjacent side of $$5$$ units and opposite side of $$12$$ units. What is the length of the hypotenuse?

Accepted Answer

$$13$$ units

Assignment 1: Algebra, Trigonometry, and Calculus Foundations for Physics

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