Motion in a Straight Line
1. What is Motion?
Motion is the change in position of an object with time. If it occurs along a straight line, it's called rectilinear motion or motion in a straight line.
2. Frame of Reference
A system used to measure the position and motion of a body. It includes:
- A reference point (origin)
- Coordinate axes (x, y, z)
- A clock to measure time
3. Rest and Motion
- Rest: Object doesn’t change position with respect to reference.
- Motion: Object changes position with respect to reference.
4. Distance and Displacement
Quantity | Distance | Displacement |
---|---|---|
Type | Scalar | Vector |
Definition | Total path length | Shortest path between two points |
Sign | Always positive | Can be +, −, or 0 |
5. Speed and Velocity
Quantity | Speed | Velocity |
---|---|---|
Type | Scalar | Vector |
Definition | Distance / Time | Displacement / Time |
Uniform | Constant speed | Constant magnitude & direction |
6. Acceleration
Rate of change of velocity with respect to time.
Formula: a = (v - u) / t
- Positive acceleration: Speeding up
- Negative acceleration: Slowing down (Retardation)
7. Types of Motion
- Uniform Motion: Equal displacement in equal intervals of time.
- Non-uniform Motion: Unequal displacement in equal time intervals.
8. Graphs of Motion
- Distance-Time Graph: Slope = speed; Curve = acceleration
- Velocity-Time Graph: Slope = acceleration; Area = displacement
9. Equations of Motion (Uniform Acceleration)
v = u + at
s = ut + (1/2)at²
v² = u² + 2as
s = (v + u)/2 × t
Where:
u
= initial velocityv
= final velocitya
= accelerationt
= times
= displacement
10. Relative Velocity
- If objects move in the same direction:
vrel = v₁ - v₂
- If in opposite directions:
vrel = v₁ + v₂
11. Free Fall
Motion under the influence of gravity alone.
- Acceleration due to gravity:
g = 9.8 m/s²
- Use motion equations with
a = g
when falling downward - Use
a = -g
when moving upward
12. Sign Conventions
- Upward or Right → Positive
- Downward or Left → Negative
- Displacement, velocity, and acceleration follow this rule
13. Instantaneous vs Average
- Average velocity: Over a time interval
- Instantaneous velocity: At a specific instant
14. Position-Time Graph
- Straight line → Uniform motion
- Curved line → Accelerated motion
- Slope = Velocity
15. Important Points
- Distance ≥ Displacement
- Speed ≥ Velocity
- Displacement can be zero; distance cannot
- Negative acceleration = Retardation
- Area under velocity-time graph = Displacement