Q: A car starts from rest and accelerates uniformly at $$3\ \mathrm{m/s^2$}$$ for $$4\ \mathrm{s}. $$What is its final velocity?

$$v = 3 \times 4 = 12\ \mathrm{m/s}$$

Q: A car is initially traveling at $$15\ \mathrm{m/s}$$ and accelerates at $$2.0\ \mathrm{m/s^2$}$$ for $$5\ \mathrm{s}. $$What is its final velocity?

$$v_x = 15 + 2 \times 5 = 25\ \mathrm{m/s}$$

Question 1

A vector $$\vec{A}$$ has a magnitude of 10 units and makes an angle of $$60^\circ$$ with the positive x-axis. What is the y-component $$A_y of $$this vector?

Accepted Answer

$$A_y = 10 \sin 60^\circ$$

Question 2

Given two vectors $$\vec{A} = (3, 4)$$ and $$\vec{B} = (-2, 0)$$, what is the magnitude of their sum $$\vec{R} = \vec{A} + \vec{B}$$?

Accepted Answer

$$\sqrt{(3+(-2))^2$ + (4+0)^2$} = \sqrt{1^2$ + 4^2$} = \sqrt{17}$$

Question 3

A car starts from rest and accelerates uniformly at $$3\ \mathrm{m/s^2$}$$ for $$4\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v = 3 	imes 4 = 12\ \mathrm{m/s}$$

Question 4

Which of the following best describes the average velocity $$v_{\mathrm{av}-x} of a $$particle moving in a straight line from $$x_1 to$$ $$x_2$$ over a time interval $$t_1 to$$ $$t_2$$?

Accepted Answer

$$v_{\mathrm{av}-x} = \frac{x_2$ - x_1$}{t_2$ - t_1$}$$

Question 5

A plane is flying at $$100\ \mathrm{km/h}$$, $$30^\circ$$ north of east. The wind is blowing at $$20\ \mathrm{km/h}$$, $$45^\circ$$ south of west. What is the x-component of the plane's velocity relative to the ground?

Accepted Answer

$$100 \cos 30^\circ - 20 \cos 225^\circ$$

Question 6

If a particle's position-time graph is a straight line with a positive slope, what can you say about its velocity?

Accepted Answer

The velocity is positive and constant.

Question 7

A runner moves from $$x_1 = 50$$\ \mathrm{m}$$ to x_2$ = -30\ \mathrm{m} in$$ $$10\ \mathrm{s}. $$What is the average velocity?

Accepted Answer

$$v_{\mathrm{av}-x} = \frac{-30 - 50}{10} = -8\ \mathrm{m/s}$$

Question 8

Which kinematic equation would you use to find the displacement $$x - x_0$ of an object under constant acceleration, given v$$_{0x}$$, v_x$, and t$?

Accepted Answer

$$x - x_0$ = \frac{1}{2}(v_{0x} + v_x)t$$

Question 9

A vector $$\vec{C}$$ has components $$C_x = -5$$ and $$C_y = -12. $$What is the magnitude of $$\vec{C}$$?

Accepted Answer

$$\sqrt{(-5)^2$ + (-12)^2$} = 13$$

Question 10

A car is initially traveling at $$15\ \mathrm{m/s}$$ and accelerates at $$2.0\ \mathrm{m/s^2$}$$ for $$5\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v_x = 15 + 2 	imes 5 = 25\ \mathrm{m/s}$$

Question 11

Which of the following statements about the direction of acceleration and velocity is correct?

Accepted Answer

If velocity and acceleration are in the same direction, the object speeds up.

Question 12

A ball is thrown straight up with an initial velocity of $$20\ \mathrm{m/s}. $$What is its velocity after $$2\ \mathrm{s}$$? (Assume $$g = 9.8\ \mathrm{m/s^2$}$$ downward.)

Accepted Answer

$$v = 20 - 9.8 	imes 2 = 0.4\ \mathrm{m/s}$$

Question 13

Which of the following is the correct formula for the x-component of a vector $$\vec{A}$$ with magnitude $$A$$ and angle $$	heta$$ from the positive x-axis?

Accepted Answer

$$A_x = A \cos 	heta$$

Question 14

A particle moves with constant acceleration. Which of the following graphs best represents its velocity versus time?

Accepted Answer

A straight line with a constant positive slope.

Question 15

A cyclist moves to the left with respect to the origin. If the positive x-direction is to the right, what is the sign of the cyclist's velocity?

Accepted Answer

Negative

Question 16

A vector in three dimensions has components $$A_x = 2$$, $$A_y = 3$$, $$A_z = 6. $$What is the magnitude of the vector?

Accepted Answer

$$\sqrt{2^2$ + 3^2$ + 6^2$} = 7$$

Question 17

A car travels at a constant velocity of $$30\ \mathrm{m/s}$$ for $$10\ \mathrm{s}. $$What is its displacement?

Accepted Answer

$$x = 30 	imes 10 = 300\ \mathrm{m}$$

College Physics I: Models, Measurements, Vectors, and Motion Along a Straight Line

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