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Motion in One Dimension
Motion in One Dimension with Constant Velocity
Motion in One Dimension with Constant Velocity
Basic Concepts
Motion in one dimension is defined as the movement of an object along a straight line (such as the x or y axis) without changing direction. When velocity is constant:
- Acceleration (a) = zero
- Velocity (v) is constant
- Distance traveled is directly proportional to time
Mathematical Equations
x(t) = x₀ + v₀t
Where:
- x₀: Initial position (m)
- v₀: Constant velocity (m/s)
- t: Time (s)
Practical Applications
1. Transportation Systems
Calculating arrival time for trains moving at constant speed between stations
2. Industrial Robots
Moving robotic arms at uniform speeds in assembly lines
3. Air Navigation
Planning aircraft routes during level flight
Motion with Acceleration
One-Dimensional Motion Simulation
Displacement Calculator
Result:
Time Calculator
Result:
Motion Equations with Constant Acceleration:
1. Displacement:
\[x(t) = x₀ + v₀t + ½at²\]
2. Velocity:
\[v(t) = v₀ + at\]
3. Final Velocity:
\[v² = v₀² + 2a(x - x₀)\]
Where:
x₀ = Initial position
v₀ = Initial velocity
a = Acceleration
t = Time
Practical Applications:
- Free-fall motion of objects
- Rocket motion during launch
- Car braking systems
- Projectile motion analysis
- Amusement park ride design (roller coasters)
When an object moves in one dimension with varying velocity, the object has acceleration which is the time rate of change of velocity
Uniform Acceleration Motion Calculation
Uniform Acceleration Motion Calculator
Results:
Acceleration: 0.00 m/s²
Displacement at desired moment: 0.00 meters
Velocity at desired moment: 0.00 m/s
Comparison of One-Dimensional Motion Types
Comparison of One-Dimensional Motion
Comparison Aspect
Motion with Constant Velocity
Motion with Uniform Acceleration
Concept
Motion of an object along a straight line with velocity that doesn't change over time
Motion of an object along a straight line with velocity changing at a constant rate
Velocity
Constant (v = v₀)
Changes linearly with time (v = v₀ + at)
Acceleration
Zero (a = 0)
Constant (a = constant)
Motion Equations
1. Displacement: X = v₀t + X₀
1. Velocity: v = v₀ + at
2. Displacement: X = v₀t + ½at² + X₀
3. v² = v₀² + 2a(X - X₀)
Graphs
- Displacement-time: Inclined straight line
- Velocity-time: Horizontal line
- Acceleration-time: Line at zero
- Displacement-time: Parabola
- Velocity-time: Inclined straight line
- Acceleration-time: Horizontal line
Free Fall in One Dimension
Free Fall in One Dimension
Motion Definition:
Motion of an object under the influence of Earth's gravity only, without air resistance.
Free Fall Equations:
1. Final Velocity:
\[ v = v₀ + gt \]
g :Acceleration due to gravity
\[g ≈ 9.8\; m/s²\]
2. Vertical Displacement:
\[Δy = v₀t + ½gt²\]
3. Velocity without knowing time:
\[v² = v₀² + 2gΔy\]
Purpose of Study:
- Understanding basics of motion with constant acceleration
- Analyzing gravity's effect on objects
- Applying motion principles in engineering projects
Galileo Galilei:
First to scientifically study free fall in the 17th century, proving equal acceleration of objects despite different masses (in vacuum).
Practical Applications:
- Parachute system design
- Calculating object fall time in construction
- Programming space simulators
- Improving air sports performance
Practical Example:
If an object falls from 100 meters height:
Time to reach ground:
\[t = sqrt {\frac {2h}{g} }≈ 4.5 \;s\]
Impact velocity:
\[v = gt ≈ 44 m/s\]
Free Fall Calculator
Free Fall Calculator
Results:
Motion in One Dimension |
Motion in One Dimension with Constant Velocity
Basic Concepts
Motion in one dimension is defined as the movement of an object along a straight line (such as the x or y axis) without changing direction. When velocity is constant:
- Acceleration (a) = zero
- Velocity (v) is constant
- Distance traveled is directly proportional to time
Mathematical Equations
Where:
- x₀: Initial position (m)
- v₀: Constant velocity (m/s)
- t: Time (s)
Practical Applications
1. Transportation Systems
Calculating arrival time for trains moving at constant speed between stations
2. Industrial Robots
Moving robotic arms at uniform speeds in assembly lines
3. Air Navigation
Planning aircraft routes during level flight
Displacement Calculator
Result:
Time Calculator
Result:
Motion Equations with Constant Acceleration:
1. Displacement: \[x(t) = x₀ + v₀t + ½at²\]
2. Velocity: \[v(t) = v₀ + at\]
3. Final Velocity: \[v² = v₀² + 2a(x - x₀)\]
Where:
x₀ = Initial position
v₀ = Initial velocity
a = Acceleration
t = Time
Practical Applications:
- Free-fall motion of objects
- Rocket motion during launch
- Car braking systems
- Projectile motion analysis
- Amusement park ride design (roller coasters)
When an object moves in one dimension with varying velocity, the object has acceleration which is the time rate of change of velocity
Uniform Acceleration Motion Calculator
Results:
Acceleration: 0.00 m/s²
Displacement at desired moment: 0.00 meters
Velocity at desired moment: 0.00 m/s
Comparison of One-Dimensional Motion
| Comparison Aspect | Motion with Constant Velocity | Motion with Uniform Acceleration |
|---|---|---|
| Concept | Motion of an object along a straight line with velocity that doesn't change over time | Motion of an object along a straight line with velocity changing at a constant rate |
| Velocity | Constant (v = v₀) | Changes linearly with time (v = v₀ + at) |
| Acceleration | Zero (a = 0) | Constant (a = constant) |
| Motion Equations |
1. Displacement: X = v₀t + X₀ |
1. Velocity: v = v₀ + at 2. Displacement: X = v₀t + ½at² + X₀ 3. v² = v₀² + 2a(X - X₀) |
| Graphs |
- Displacement-time: Inclined straight line - Velocity-time: Horizontal line - Acceleration-time: Line at zero |
- Displacement-time: Parabola - Velocity-time: Inclined straight line - Acceleration-time: Horizontal line |
Free Fall in One Dimension
Motion Definition:
Motion of an object under the influence of Earth's gravity only, without air resistance.
Free Fall Equations:
g :Acceleration due to gravity \[g ≈ 9.8\; m/s²\]
Purpose of Study:
- Understanding basics of motion with constant acceleration
- Analyzing gravity's effect on objects
- Applying motion principles in engineering projects
Galileo Galilei:
First to scientifically study free fall in the 17th century, proving equal acceleration of objects despite different masses (in vacuum).
Practical Applications:
- Parachute system design
- Calculating object fall time in construction
- Programming space simulators
- Improving air sports performance
Practical Example:
If an object falls from 100 meters height:
Time to reach ground:
\[t = sqrt {\frac {2h}{g} }≈ 4.5 \;s\]
Impact velocity:
\[v = gt ≈ 44 m/s\]
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