Learning Objectives
- Understand the concepts of distance, displacement, speed, velocity, and acceleration
- Plot and interpret distance-time and velocity-time graphs
- Derive and apply the three equations of motion
- Understand uniform circular motion
Key Concepts
Distance and Displacement
Distance: Total path length covered by an object. It is a scalar quantity (has only magnitude). Always positive or zero.
Displacement: Shortest distance between the initial and final positions, along with direction. It is a vector quantity (has magnitude and direction). Can be positive, negative, or zero.
Displacement ≤ Distance always.
Speed and Velocity
Speed: Distance covered per unit time. Speed = Distance / Time. Scalar quantity. SI unit: m/s.
Average speed: Total distance / Total time taken.
Velocity: Displacement per unit time. Velocity = Displacement / Time. Vector quantity. SI unit: m/s.
Uniform velocity: Equal displacement in equal time intervals in the same direction.
Acceleration
Acceleration: Rate of change of velocity. a = (v - u) / t
SI unit: m/s². Positive acceleration means speeding up; negative acceleration (deceleration/retardation) means slowing down.
Uniform acceleration: Velocity changes by equal amounts in equal time intervals.
Equations of Motion (Uniformly Accelerated Motion)
Where u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement:
- First equation: v = u + at
- Second equation: s = ut + (1/2)at²
- Third equation: v² = u² + 2as
Graphical Representation
Distance-Time Graph: Straight line with positive slope = uniform speed. Curve = non-uniform speed. Slope = speed.
Velocity-Time Graph: Straight line parallel to time axis = uniform velocity (zero acceleration). Straight line with slope = uniform acceleration. Area under the graph = distance covered. Slope = acceleration.
Deriving Equations from Graphs
From velocity-time graph: the area under the curve gives displacement. The first equation is derived from the definition of acceleration. The second and third equations can be derived from the velocity-time graph using area calculations.
Uniform Circular Motion
When an object moves in a circular path with constant speed, it has uniform circular motion. The velocity changes continuously because the direction changes, so the object is always accelerating.
Speed = 2πr / T where r is radius and T is the time period (time for one complete revolution).
Summary
Motion is described using distance, displacement, speed, velocity, and acceleration. Three equations of motion apply to uniformly accelerated motion. Graphical methods using distance-time and velocity-time graphs help visualise and calculate motion parameters. In uniform circular motion, speed is constant but velocity changes due to change in direction.
Important Terms
- Distance: Total path length (scalar)
- Displacement: Shortest path between start and end points (vector)
- Speed: Rate of covering distance (scalar)
- Velocity: Rate of change of displacement (vector)
- Acceleration: Rate of change of velocity
- Uniform Circular Motion: Motion in a circle at constant speed
Quick Revision
- v = u + at; s = ut + (1/2)at²; v² = u² + 2as
- Slope of distance-time graph = speed
- Slope of velocity-time graph = acceleration
- Area under velocity-time graph = distance
- Circular motion at constant speed: direction changes, so velocity changes