Step | Formula Derivation | Reasoning |
---|---|---|

1 | d = v_i t + \frac{1}{2} g t^2 | This is the kinematic equation for distance (d), where v_i is the initial velocity, t is the time, and g is the gravitational acceleration. |

2 | 17 = 15 \times 1 + \frac{1}{2} g \times 1^2 | Substitute d = 17 m, v_i = 15 m/s, and t = 1 s into the equation. |

3 | 17 = 15 + \frac{1}{2} g | Simplify the equation. |

4 | \frac{1}{2} g = 17 – 15 | Rearrange to solve for g. |

5 | g = 2 \times 2 | Simplify and solve for g. |

6 | g = 4 m/s² | The gravitational acceleration is 4 m/s². |

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- Statistics

Intermediate

Conceptual

MCQ

An object is projected vertically upward from ground level. It rises to a maximum height H . If air resistance is negligible, which of the following must be true for the object when it is at a height H/2 ?

- 1D Kinematics, Energy

Beginner

Conceptual

MCQ

Can an object’s average velocity equal zero when object’s speed is greater than zero?

- 1D Kinematics

Advanced

Mathematical

MCQ

An object undergoes constant acceleration. Starting from rest, the object travels 5 m in the first second. Then it travels 15 meters in the next second. What additional distance will be covered in the third second?

- 1D Kinematics

Intermediate

Mathematical

FRQ

You throw a rock straight up with an initial velocity of 5.0 m/s.

- 1D Kinematics

Advanced

Mathematical

FRQ

A coin is dropped from a hot air-balloon that is 250 m above the ground rising at 11 m/s upwards. For the coin, assume up is positive and find the following:

- 1D Kinematics

Intermediate

Mathematical

GQ

A block starts from rest at the top of a 50° incline. The coefficient of kinetic friction between the block and the incline is 0.4. If the block reaches a velocity of 7 m/s at the bottom of the incline, what is the length of the incline?

- 1D Kinematics, Friction, Inclines, Linear Forces

Beginner

Conceptual

MCQ

The displacement x of an object moving in one dimension is shown above as a function of time t. The velocity of this object must be

- 1D Kinematics, Motion Graphs

Advanced

Mathematical

GQ

*v* versus time *t* for an object in linear motion. Which of the following is a possible graph of position *x* versus time *t* for this object?

- 1D Kinematics, Motion Graphs

Intermediate

Mathematical

GQ

A driver is driving at 40m/s when the light turns red in front of her. It takes the driver 0.9 s to react and hit the brakes. After this, the car slows with an acceleration of 3.5 \, \text{m/s}^2. What is the total distance traveled by the car?

- 1D Kinematics

Advanced

Mathematical

FRQ

Two students are on a balcony 19.6 m above the street. One student throws a ball vertically downward at 14.7 m/s. At the same instant, the other student throws a ball vertically upward at the same speed. The second ball just misses the balcony on the way down.

- 1D Kinematics

g = 4 m/s²

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Kinematics | Forces |
---|---|

\Delta x = v_i t + \frac{1}{2} at^2 | F = ma |

v = v_i + at | F_g = \frac{G m_1m_2}{r^2} |

a = \frac{\Delta v}{\Delta t} | f = \mu N |

R = \frac{v_i^2 \sin(2\theta)}{g} |

Circular Motion | Energy |
---|---|

F_c = \frac{mv^2}{r} | KE = \frac{1}{2} mv^2 |

a_c = \frac{v^2}{r} | PE = mgh |

KE_i + PE_i = KE_f + PE_f |

Momentum | Torque and Rotations |
---|---|

p = m v | \tau = r \cdot F \cdot \sin(\theta) |

J = \Delta p | I = \sum mr^2 |

p_i = p_f | L = I \cdot \omega |

Simple Harmonic Motion |
---|

F = -k x |

T = 2\pi \sqrt{\frac{l}{g}} |

T = 2\pi \sqrt{\frac{m}{k}} |

Constant | Description |
---|---|

g | Acceleration due to gravity, typically 9.8 , \text{m/s}^2 on Earth’s surface |

G | Universal Gravitational Constant, 6.674 \times 10^{-11} , \text{N} \cdot \text{m}^2/\text{kg}^2 |

\mu_k and \mu_s | Coefficients of kinetic (\mu_k) and static (\mu_s) friction, dimensionless. Static friction (\mu_s) is usually greater than kinetic friction (\mu_k) as it resists the start of motion. |

k | Spring constant, in \text{N/m} |

M_E = 5.972 \times 10^{24} , \text{kg} | Mass of the Earth |

M_M = 7.348 \times 10^{22} , \text{kg} | Mass of the Moon |

M_M = 1.989 \times 10^{30} , \text{kg} | Mass of the Sun |

Variable | SI Unit |
---|---|

s (Displacement) | \text{meters (m)} |

v (Velocity) | \text{meters per second (m/s)} |

a (Acceleration) | \text{meters per second squared (m/s}^2\text{)} |

t (Time) | \text{seconds (s)} |

m (Mass) | \text{kilograms (kg)} |

Variable | Derived SI Unit |
---|---|

F (Force) | \text{newtons (N)} |

E, PE, KE (Energy, Potential Energy, Kinetic Energy) | \text{joules (J)} |

P (Power) | \text{watts (W)} |

p (Momentum) | \text{kilogram meters per second (kgm/s)} |

\omega (Angular Velocity) | \text{radians per second (rad/s)} |

\tau (Torque) | \text{newton meters (Nm)} |

I (Moment of Inertia) | \text{kilogram meter squared (kgm}^2\text{)} |

f (Frequency) | \text{hertz (Hz)} |

General Metric Conversion Chart

Conversion Example

Example of using unit analysis: Convert 5 kilometers to millimeters.

Start with the given measurement:

`\text{5 km}`

Use the conversion factors for kilometers to meters and meters to millimeters:

`\text{5 km} \times \frac{10^3 \, \text{m}}{1 \, \text{km}} \times \frac{10^3 \, \text{mm}}{1 \, \text{m}}`

Perform the multiplication:

`\text{5 km} \times \frac{10^3 \, \text{m}}{1 \, \text{km}} \times \frac{10^3 \, \text{mm}}{1 \, \text{m}} = 5 \times 10^3 \times 10^3 \, \text{mm}`

Simplify to get the final answer:

`\boxed{5 \times 10^6 \, \text{mm}}`

Prefix | Symbol | Power of Ten | Equivalent |
---|---|---|---|

Pico- | p | 10^{-12} | 0.000000000001 |

Nano- | n | 10^{-9} | 0.000000001 |

Micro- | µ | 10^{-6} | 0.000001 |

Milli- | m | 10^{-3} | 0.001 |

Centi- | c | 10^{-2} | 0.01 |

Deci- | d | 10^{-1} | 0.1 |

(Base unit) | – | 10^{0} | 1 |

Deca- or Deka- | da | 10^{1} | 10 |

Hecto- | h | 10^{2} | 100 |

Kilo- | k | 10^{3} | 1,000 |

Mega- | M | 10^{6} | 1,000,000 |

Giga- | G | 10^{9} | 1,000,000,000 |

Tera- | T | 10^{12} | 1,000,000,000,000 |

- Some answers may be slightly off by 1% depending on rounding, etc.
- Answers will use different values of gravity. Some answers use 9.81 m/s
^{2}, and other 10 m/s^{2 }for calculations. - Variables are sometimes written differently from class to class. For example, sometime initial velocity v_i is written as u ; sometimes \Delta x is written as s .
- Bookmark questions that you can’t solve so you can come back to them later.
- Always get help if you can’t figure out a problem. The sooner you can get it cleared up the better chances of you not getting it wrong on a test!

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