Motion in one dimension refers to the movement of an object along a straight line. It can be described by various physical quantities such as displacement, velocity, and acceleration. Here is a document summarizing the key concepts and equations related to motion in one dimension:

Motion in One Dimension

1. Displacement (Δx):
- The change in position of an object.
- It is a vector quantity, indicating both magnitude and direction.

2. Average Velocity (v):
- The displacement divided by the time taken.
- v = Δx / Δt
- Unit: m/s (meters per second)

3. Instantaneous Velocity (v):
- The velocity at a specific instant in time.
- It is the derivative of the displacement with respect to time.
- v = dx / dt

4. Average Speed (s):
- The total distance traveled divided by the time taken.
- s = total distance / Δt
- Unit: m/s (meters per second)

5. Acceleration (a):
- The rate of change of velocity.
- a = Δv / Δt
- It is a vector quantity, indicating both magnitude and direction.
- Unit: m/s² (meters per second squared)

6. Equations of Motion:
- These equations relate displacement, velocity, acceleration, and time for an object in motion.

a. v = u + at
- Final velocity (v) = Initial velocity (u) + (acceleration × time)

b. Δx = ut + (1/2)at²
- Displacement (Δx) = Initial velocity (u) × time + (1/2) × (acceleration × time²)

c. v² = u² + 2aΔx
- Final velocity squared (v²) = Initial velocity squared (u²) + 2 × (acceleration × displacement)

d. Δx = (v + u) / 2 × t
- Displacement (Δx) = (Initial velocity + Final velocity) / 2 × time

7. Graphs of Motion:
- The relationship between displacement, velocity, and acceleration can be represented graphically.

a. Displacement-Time Graph:
- The slope of the graph represents velocity.
- The area under the graph represents displacement.

b. Velocity-Time Graph:
- The slope of the graph represents acceleration.
- The area under the graph represents displacement.

c. Acceleration-Time Graph:
- The area under the graph represents change in velocity.

Remember to apply the appropriate sign conventions (+/-) for direction while solving numerical problems. Practice using these equations and graphs to analyze and solve problems related to motion in one dimension.

For more detailed explanations, solved examples, and additional practice questions, you can refer to the Physics Class 11 notes, videos, and resources available online or in textbooks.

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