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| Concept/Formula | Definition/Equation | When to Use |
|---|---|---|
| Standard Form | , | Expressing very large/small numbers |
| Nautical Mile (NM) | 1 NM = 1.852 km | Air navigation distance |
| Area of a Rectangle | Calculating area of rectangular surfaces | |
| Volume of a Cylinder | Calculating volume of cylindrical objects | |
| Elapsed Time | Calculating flight duration | |
| Speed Conversion | Converting between speed units |
Type A: Converting to Standard Form
Setup: "Given a large or small number."
Method: Move the decimal point to have one digit to the left and adjust the exponent accordingly.
Example: 5300000 = 5.3 x 10^6
Type B: Calculating Elapsed Time
Setup: "Given start and end times."
Method: Subtract the start time from the end time.
Example: Start: 14:20 UTC, End: 18:55 UTC. Elapsed Time = 4 hours 35 minutes.
Problem: Convert 0.000000053 to standard form. Steps:
"โAnswer: 5.3 x 10^-8
| Concept/Formula | Definition/Equation | When to Use |
|---|---|---|
| Speed | Calculating average speed | |
| Velocity | Calculating average velocity | |
| Acceleration | Calculating uniform acceleration | |
| Equation of Motion 1 | Finding final velocity | |
| Equation of Motion 2 | Finding displacement |
Type A: Calculating Acceleration
Setup: "Given initial velocity, final velocity, and time."
Method: Use the formula a = (v - u) / t.
Example: u = 10 m/s, v = 25 m/s, t = 5 s. a = (25 - 10) / 5 = 3 m/sยฒ.
Type B: Interpreting Distance-Time Graphs
Setup: "Given a distance-time graph."
Method: The gradient of the line represents speed. A flat section indicates no speed (stopped).
Example: A steeper graph indicates a greater speed.
Problem: A car accelerates from 10 m/s to 25 m/s in 5 seconds. Calculate the acceleration. Steps:
"โAnswer: 3 m/sยฒ
| Concept/Formula | Definition/Equation | When to Use |
|---|---|---|
| Newton's Second Law | Calculating force, mass, or acceleration | |
| Weight | Calculating the weight of an object | |
| Newton's Third Law | Action-Reaction Pairs | Identifying forces acting on different objects |
| Inertia | Resistance to change in motion | Explaining why objects resist changes in velocity |
Type A: Calculating Force
Setup: "Given mass and acceleration."
Method: Use the formula F = ma.
Example: m = 5 kg, a = 2 m/sยฒ. F = 5 * 2 = 10 N.
Type B: Identifying Action-Reaction Pairs
Setup: "Given a scenario with interacting objects."
Method: Identify the force exerted by one object on another and the equal and opposite force exerted back.
Example: A rocket launching: Rocket exerts force on exhaust gases, exhaust gases exert equal and opposite force on rocket.
Problem: A 5 kg object accelerates at 2 m/sยฒ. Calculate the force acting on it. Steps:
"โAnswer: 10 N
| Concept/Formula | Definition/Equation | When to Use |
|---|---|---|
| Acceleration due to Gravity | Calculating motion of falling objects | |
| Distance in Free Fall | Calculating distance fallen from rest | |
| Terminal Velocity | Air resistance = Weight | Determining constant velocity during fall |
Type A: Calculating Distance in Free Fall
Setup: "Given time and initial velocity (usually 0)."
Method: Use the formula s = (1/2)gtยฒ.
Example: t = 3 s. s = 0.5 * 9.8 * 3ยฒ = 44.1 m.
Type B: Understanding Terminal Velocity
Setup: "Given a scenario where air resistance is significant."
Method: Air resistance increases with speed until it equals the object's weight. At this point, acceleration is zero, and the object falls at a constant velocity.
Example: A skydiver reaches terminal velocity when air resistance equals their weight.
Problem: Calculate the distance a ball falls in 3 seconds, starting from rest. Steps:
"โAnswer: 44.1 m
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