Q: Gold has a density of $19.32\ \text{g/cm}^3$. What is the length of a side of a gold cube of mass $27.63\ \text{g}$?

$1.127 \times 10^{-2}\ \text{m}$

Q: Refer to the circular motion diagram (image_6). If the object moves counterclockwise at $v = 5\ \text{m/s}$ and $\vec{r} = (3\ \text{m}) \hat{j}$, what is the centripetal acceleration vector?

$(-8.33\ \text{m/s}^2) \hat{j}$

Question 1

A car's velocity is given by $v = At^2 + Bt^3$, where $t$ is in seconds. What are the units of $A$ and $B$?

Accepted Answer

$A$: m/s^2 ; $B$: m/s^3$

Question 2

The velocity of a particle is given by $v = At^2 + Bt + C + D/t$, where $t$ is in seconds. Which coefficient has the dimensions of acceleration?

Accepted Answer

A

Question 3

The acceleration of an object falling through the atmosphere is $a = g - c v^2$. What are the dimensions of the constant $c$?

Accepted Answer

$m^{-1}$

Question 4

Gold has a density of $19.32\ 	ext{g/cm}^3$. What is the length of a side of a gold cube of mass $27.63\ 	ext{g}$?

Accepted Answer

$1.127 	imes 10^{-2}\ 	ext{m}$

Question 5

A soda can has radius $R = 3.05\ 	ext{cm}$ and height $h = 10.95\ 	ext{cm}$. Filled with water of density $ho = 1.00\ 	ext{g/cm}^3$, what is the mass of water in kilograms?

Accepted Answer

0.225 kg

Question 6

Lithium has a density of $0.53\ 	ext{g/cm}^3$. What is the mass of a cube made of lithium that measures $2.0\ 	ext{m}$ on each side?

Accepted Answer

1060 kg

Question 7

The position of an object is given by $x(t) = (2\ 	ext{m/s}^3) t^3$. What is its average velocity between $t_1 = 2\ 	ext{s}$ and $t_2 = 3\ 	ext{s}$?

Accepted Answer

54 m/s

Question 8

You run $450\ 	ext{m}$ at $5.60\ 	ext{m/s}$, then walk $350\ 	ext{m}$ at $1.40\ 	ext{m/s}$. What is your average speed for the entire journey?

Accepted Answer

3.50 m/s

Question 9

A car accelerates uniformly from rest to $35.8\ 	ext{m/s}$ in $15\ 	ext{s}$. How much distance is covered?

Accepted Answer

537 m

Question 10

A rock is thrown down a well with initial velocity $v_0 = -11\ 	ext{m/s}$. The well is $55\ 	ext{m}$ deep. With what speed does the rock strike the bottom?

Accepted Answer

60.6 m/s

Question 11

A ball is thrown upwards from $y_0 = 0\ 	ext{m}$ and reaches $y_1 = 13\ 	ext{m}$ in $t_1 = 0.4\ 	ext{s}$. What is the maximum height the ball will reach?

Accepted Answer

21.7 m

Question 12

Two cars drive towards each other. Car 1 starts at $x = 0$ with $v_1 = +5\ 	ext{m/s}$, car 2 is $120\ 	ext{m}$ away with $a_2 = -2\ 	ext{m/s}^2$. At what time will they pass?

Accepted Answer

6.4 s

Question 13

Refer to the first velocity-time graph (image_1). How far does the car travel between $t = 2\ 	ext{s}$ and $t = 9\ 	ext{s}$?

Accepted Answer

48 m

Question 14

Refer to the second velocity-time graph (image_2). What is the displacement of the particle between $t = 2\ 	ext{s}$ and $t = 7\ 	ext{s}$?

Accepted Answer

$\Delta x = -6\ 	ext{m}$

Question 15

For the vectors in image_3, which statement is true?

Accepted Answer

$\vec{C} \cdot \vec{A} < 0$

Question 16

A basketball player (image_4) shoots the ball at $40^\circ$ above the horizontal with a speed of $7.6\ 	ext{m/s}$ from a height of $2.0\ 	ext{m}$ to a basket at $3.05\ 	ext{m}$. How long is the ball in the air?

Accepted Answer

0.81 s

Question 17

A ball is thrown toward a wall (image_5) at $21.0\ 	ext{m/s}$ and $	heta_0 = 39.0^\circ$. The wall is $d = 18.0\ 	ext{m}$ away. At what vertical distance above the release point does the ball hit the wall?

Accepted Answer

5.8 m

Question 18

A stone is attached to a cord and executes uniform circular motion. If the cord’s length is tripled but the stone maintains the original centripetal acceleration, what is the new speed?

Accepted Answer

$v\sqrt{3}$

Question 19

Refer to the circular motion diagram (image_6). If the object moves counterclockwise at $v = 5\ 	ext{m/s}$ and $\vec{r} = (3\ 	ext{m}) \hat{j}$, what is the centripetal acceleration vector?

Accepted Answer

$(-8.33\ 	ext{m/s}^2) \hat{j}$

Guidance for 1-D Kinematics Graphical Methods: Calculating Displacement from Velocity-Time Graphs

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