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

$$\vec{C} \cdot \vec{A} \u003c 0$$

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 $$\$$theta_0$$ = 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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