Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the expression for its horizontal range (assuming level ground)?

$$R = \frac{v_0$^2 \sin(2\theta)}{g}$$

Question 1

A car travels 120 km in 2 hours. What is its average speed in meters per second?

Accepted Answer

$$16.7\ 	ext{m/s}$$

Question 2

Which of the following correctly expresses the vector $$\vec{A}$$ with magnitude 5 and direction 30° above the x-axis in terms of unit vectors?

Accepted Answer

$$\vec{A} = 5\cos(30^\circ)\hat{i} + 5\sin(30^\circ)\hat{j}$$

Question 3

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 4

Which metric prefix represents $$10^{-6}$$?

Accepted Answer

micro

Question 5

A ball is thrown vertically upward with an initial velocity of $$20\ 	ext{m/s}. $$Ignoring air resistance, how long does it take to reach its maximum height?

Accepted Answer

$$2\ 	ext{s}$$

Question 6

Which equation gives the position $$x as a $$function of time $$t$$ for an object moving with constant acceleration $$a$$ and initial velocity $$v_0$$?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 7

If $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = 4\hat{i} - \hat{j}$$, what is $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

$$11$$

Question 8

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the expression for its horizontal range (assuming level ground)?

Accepted Answer

$$R = \frac{v_0$^2 \sin(2	heta)}{g}$$

Question 9

Which of the following is NOT a vector quantity?

Accepted Answer

Speed

Question 10

A cyclist increases her speed from $$5\ 	ext{m/s} to$$ $$15\ 	ext{m/s} in$$ $$4\ 	ext{s}. $$What is her average acceleration?

Accepted Answer

$$2.5\ 	ext{m/s}^2$$

Question 11

The dot product of two vectors $$\vec{A}$$ and $$\vec{B} is $$zero. What does this imply about their directions?

Accepted Answer

They are perpendicular

Question 12

A stone is dropped from a height of $$45\ 	ext{m}. $$How long does it take to reach the ground? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$3.03\ 	ext{s}$$

Question 13

Which of the following best describes the difference between distance and displacement?

Accepted Answer

Distance is the total path traveled; displacement is the shortest path between two points.

Question 14

If the velocity vs. time graph of an object is a straight line with positive slope, what can be said about the object's acceleration?

Accepted Answer

Acceleration is constant and positive.

Question 15

A vector $$\vec{C} is $$multiplied by a scalar $$k = -2. $$What happens to the direction and magnitude of $$\vec{C}$$?

Accepted Answer

Magnitude doubles, direction reverses.

Question 16

Which formula gives the tangential acceleration $$a_t$$ for an object in circular motion with changing speed?

Accepted Answer

$$a_t = \frac{dv}{dt}$$

Question 17

A particle moves along a path described by $$x(t) = 2t^2$ and y(t) = 3t$. What is its velocity vector at t = 2$$\ 	ext{s}$$?

Accepted Answer

$$\vec{v} = 8\hat{i} + 3\hat{j}$$

Question 18

Which operation between two vectors results in a vector perpendicular to both original vectors?

Accepted Answer

Cross product

Question 19

A car moves in a circle of radius $$10\ 	ext{m} at a $$constant speed of $$5\ 	ext{m/s}. $$What is its centripetal acceleration?

Accepted Answer

$$2.5\ 	ext{m/s}^2$$

PHY 251 Exam 1 Study Guide: Units, Vectors, and Kinematics

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