Q: The density of silver is 10.5 g/cm$$^{3}. $$What is this density in SI units (kg/m$$^{3}$$)?

$$1.05 \times 10$$^{4}$$ kg/m$$^{3}$

Q: For the vectors in the previous question, what angle does $$2\vec{A} - \vec{B}$$ make with the $$+x$$ axis?

$$\tan$$^{-1}$$\left(\frac{3\sqrt{3} + 18/5}{24/5 - 3}\right)$$

Question 1

The density of silver is 10.5 g/cm$$^{3}. $$What is this density in SI units (kg/m$$^{3}$$)?

Accepted Answer

$$1.05 	imes 10$$^{4}$$ kg/m$$^{3}$

Question 2

A solid cylinder has volume $$V = \pi r$$^{2}$$ h. If $$the radius is doubled and the height is halved, by what factor does the mass change (assuming constant density)?

Accepted Answer

The mass increases by a factor of 4

Question 3

A rocket starts from rest. For the first 10.0 s its acceleration is $$a_{y} = 3t (m/s$^{2}). $$How high is the rocket at $$t = 10.0 s$$?

Accepted Answer

$$500 m$$

Question 4

A car accelerates from rest to $$72 km/h in$$ $$10 s. $$Compute the average acceleration during this interval.

Accepted Answer

$$2.0$$ $$m/s^{2}$

Question 5

A shot is thrown at $$12.0 m/s at$$ $$53^{\circ}$$ above horizontal. It lands $$2.00 s $$later. How far does it travel horizontally?

Accepted Answer

$$14.4 m$$

Question 6

A moving sidewalk travels at $$1.5 m/s $$and is $$30.0 m $$long. A woman walks at $$2.0 m/s $$relative to the sidewalk opposite its motion. How long does she take to cross?

Accepted Answer

$$20 s$$

Question 7

A bird’s position is $$x(t) = 30.0 + 12.0t - 0.050t$$^{3}$$. Find the instantaneous velocity at t = 8.00$ s.

Accepted Answer

$$-2.4 m/s$$

Question 8

A 1.0 m string makes a constant angle of $$37^{\circ}$$ with the vertical while a ball moves in a horizontal circle. The period is $$2.0 s. $$Find the radial acceleration (leave your answer in terms of $$\pi).$$

Accepted Answer

$$0.60\pi$$^{2}$$

Question 9

Vector $$\vec{A}$$ has magnitude $$5.0 m $$and makes an angle of $$60^{\circ}$$ with the positive x-axis. Write $$\vec{A} in $$terms of $$\hat{i}$$ and $$\hat{j}.$$

Accepted Answer

$$2.5\hat{i} + 5\frac{\sqrt{3}}{2}\hat{j}$$

Question 10

A jet plane pulls out of a downward dive. The bottom portion of the flight path is a quarter circle of radius $$300 m. $$Medical studies show that pilots lose consciousness if the upward acceleration exceeds $$5.5g. $$What minimum speed must the plane have at the bottom of the dive for the pilot to black out? (Take $$g = 10 m/s$^{2})$$

Accepted Answer

$$130 m/s$$

Question 11

Two stones are thrown vertically upward from the ground, one with three times the initial speed of the other. If the faster stone takes $$10 s to $$return to the ground, how long does the slower stone take to return?

Accepted Answer

$$\frac{10}{3} s$$

Question 12

A dog in an open field is at rest under a tree at $$t = 0$$ and starts running. Its acceleration is $$\vec{a}(t) = 0.5\hat{i} - t\hat{j} (m/s$^{2}). $$What is the velocity vector $$\vec{v}(t)$$?

Accepted Answer

$$0.5t\hat{i} - \frac{1}{2}t$$^{2}$$\hat{j}$$

Question 13

A drive between San Diego and Los Angeles takes $$2 h at$$ $$100 km/h. If $$heavy traffic reduces the average speed to $$72 km/h$$, how much longer does the trip take?

Accepted Answer

$$50$$ min

Question 14

A vector $$\vec{A} is$$ $$3.0 cm at$$ $$60^{\circ}$$ above the horizontal. Vector $$\vec{B} is$$ $$6.0 cm at$$ $$37^{\circ}$$ below the horizontal. Use $$\sin 37$$^{\circ}$$ = \frac{3}{5}$$ and $$\cos 37$$^{\circ}$$ = \frac{4}{5}. $$What is $$|\vec{A} + \vec{B}|$$?

Accepted Answer

$$\sqrt{\left(\frac{3}{2} + \frac{24}{5}\$$right)^{2}$$ + \left(\frac{3\sqrt{3}}{2} - \frac{18}{5}\$$right)^{2}$$}$$

Question 15

For the vectors in the previous question, what angle does $$2\vec{A} - \vec{B}$$ make with the $$+x$$ axis?

Accepted Answer

$$	an$$^{-1}$$\left(\frac{3\sqrt{3} + 18/5}{24/5 - 3}ight)$$

Question 16

A dog in an open field is at rest under a tree at $$t = 0$$ and starts running. Its acceleration is $$\vec{a}(t) = 0.5\hat{i} - t\hat{j} (m/s$^{2}). $$What is the position vector $$\vec{r}(t)$$ measured from the tree?

Accepted Answer

$$\frac{1}{4}t$$^{2}$$\hat{i} - \frac{1}{6}t$$^{3}$$\hat{j}$$

Question 17

A jet plane pulls out of a downward dive. The bottom portion of the flight path is a quarter circle of radius $$300 m. $$Medical studies show that pilots lose consciousness if the upward acceleration exceeds $$5.5g. $$What is this speed in mph? (Take $$g = 10 m/s$^{2}$$ and $$1 m/s$$ $$= 2.24$$ mph)

Accepted Answer

$$291$$ mph

Question 18

A dog in an open field is at rest under a tree at $$t = 0$$ and starts running. Its acceleration is $$\vec{a}(t) = 0.5\hat{i} - t\hat{j} (m/s$^{2}). $$How far is the dog from the tree at $$t = 5.00 s$$? (Compute $$|\vec{r}(t = 5.00)|$$ and leave your answer in radical form.)

Accepted Answer

$$\sqrt{25/4 + 125/36} m$$

Physics with Calculus Exam I Study Guidance (Chapters 1–3)

Study Guide - Practice Questions

Study Guide - Flashcards