Distance, Speed and Acceleration
Key Quantities
- Distance (s): how far an object travels, regardless of direction. Scalar. Unit: m.
- Displacement: distance in a specified direction. Vector.
- Speed (v): rate of change of distance. Scalar. v = d/t.
- Velocity: speed in a specified direction. Vector.
- Acceleration (a): rate of change of velocity. a = Δv/t = (v−u)/t. Unit: m/s².
Equations of Motion (WJEC Unit 1)
For uniform (constant) acceleration:
- v = u + at (final velocity = initial + acceleration × time)
- s = ut + ½at² (displacement = initial velocity × time + ½ × acceleration × time²)
- v² = u² + 2as (relates velocities and displacement without time)
- s = ½(u + v)t (displacement = average velocity × time)
Where: u = initial velocity (m/s), v = final velocity (m/s), a = acceleration (m/s²), t = time (s), s = displacement (m).
Distance-Time Graphs
- Horizontal line: object is stationary (distance not changing).
- Straight line with positive slope: constant speed. Gradient = speed.
- Curve (steepening): accelerating.
- Curve (flattening): decelerating.
Speed from d-t graph = gradient = Δdistance/Δtime.
Velocity-Time Graphs
- Horizontal line: constant velocity (zero acceleration).
- Straight line with positive slope: uniform acceleration. Gradient = acceleration.
- Straight line with negative slope: uniform deceleration. Gradient = acceleration (negative).
- Area under graph = displacement (distance if always positive velocity).
Acceleration from v-t graph = gradient = Δvelocity/Δtime.
Acceleration Due to Gravity
On Earth, g ≈ 10 m/s² (or 9.8 m/s²). A falling object (ignoring air resistance) accelerates at 10 m/s²; it gains 10 m/s of speed every second.
Terminal velocity: when drag force = weight, acceleration = 0 and the object falls at constant velocity. Skydivers reach terminal velocity at ~55 m/s (with arms/legs out) or ~80 m/s (diving).
WJEC Required Practical: Investigating Motion
Students use a light gate + data logger (or ticker tape + ticker timer) to measure velocity at different points to calculate acceleration. Plotting v-t gives a straight line whose gradient is a.
⚠Common mistakes
- Gradient on a d-t graph = speed, not acceleration: acceleration is the gradient of a v-t graph.
- Area on a v-t graph = displacement: students sometimes think area = acceleration.
- Forgetting to square in v² = u² + 2as: double-check the algebra.
- Speed vs velocity: speed is a scalar (magnitude only); velocity is a vector (has direction). An object can travel at constant speed but changing velocity (circular motion).
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