Motion and Uncertainty Analysis - Vocabulary Flashcards

Vocabulary flashcards covering key terms from the lecture notes on motion, uncertainty, SUVAT, graphs, stopping distances, and projectiles.

Distance

Total length travelled from one position to another; a scalar quantity.

Displacement

The shortest or straight-line distance from start to end in a given direction; a vector quantity.

Speed

Rate of distance covered; speed = distance ÷ time; scalar.

Velocity

Rate of displacement; velocity = displacement ÷ time; has magnitude and direction.

Scalar

Quantities with only magnitude, such as distance or speed.

Vector

Quantities with magnitude and direction, such as displacement or velocity.

Acceleration

Rate of change of velocity; units m/s^2; positive when speeding up, negative when slowing down.

SUVAT

Set of variables (s, u, v, a, t) and equations of motion for constant acceleration.

Displacement-time graph

Plot of displacement versus time; gradient gives velocity.

Velocity-time graph

Plot of velocity versus time; gradient gives acceleration; area under the curve gives displacement.

Distance-time graph gradient

Equals speed.

S = ut + 1/2 at^2

SUVAT equation for displacement with constant acceleration.

V^2 = U^2 + 2aS

SUVAT equation linking final and initial velocity, acceleration and displacement.

V = U + a t

SUVAT equation relating final velocity, initial velocity, acceleration and time.

S = (U + V)/2 × t

SUVAT equation for displacement when time is known.

Stopping distance

Total distance from seeing a hazard to stopping; = thinking distance + braking distance.

Thinking distance

Distance travelled during driver reaction time; approximately speed × reaction time.

Braking distance

Distance travelled while braking from initial speed to rest; can be found from v^2 = u^2 + 2as.

Reaction time

Time taken to respond to a hazard; used to calculate thinking distance.

Factors affecting stopping distance

Drugs, road conditions, distractions, speed, car condition, etc.

Gradient (distance-time graph)

Gradient equals speed on a distance-time graph.

Gradient (velocity-time graph)

Gradient equals acceleration on a velocity-time graph.

Area under velocity-time graph

Represents displacement; integral of velocity over time.

Area under acceleration-time graph

Represents change in velocity; integral of acceleration over time.

Absolute uncertainty

The base uncertainty of a single measurement, often linked to instrument resolution.

Percentage uncertainty

Absolute uncertainty expressed as a percentage of the measured value.

Random error

Spread of measured values around the true value; reducible by repeating measurements.

Systematic error

A constant bias in measurements due to methods or instruments; not reduced by repeats.

Zero error

A type of systematic error where a measuring system reads nonzero when true value is zero.

Worst-fit line

A line inside error bars that yields the maximum/minimum possible gradient.

Percentage difference

(Measured value − True value) ÷ True value × 100%.

Horizontal component of velocity (projectiles)

u cos θ for a projectile launched at angle θ.

Vertical component of velocity (projectiles)

u sin θ; changes under gravitational acceleration.

Projectile motion

Motion with perpendicular horizontal and vertical components; horizontal velocity is constant (ignoring air resistance) and vertical velocity changes due to gravity.

Independence of motions (projectiles)

Horizontal and vertical motions do not affect each other.

g (gravity)

Acceleration due to gravity, approximately 9.81 m/s^2 downward.

Angle of projection (θ)

Angle between initial velocity vector and the horizontal.

Range (projectiles)

Horizontal distance travelled by a projectile before landing.

Displacement-time vs velocity-time relationship

Displacement-time gradient gives velocity; velocity-time gradient gives acceleration.

Error bars

Graphical representation of the absolute uncertainty in measurements.

Worst fit gradient vs best fit gradient

Worst fit gradient is the maximum/minimum gradient within uncertainty; best fit is the central gradient.

Momentum of graph conversion

Understanding the conversions between displacement-time, velocity-time, and acceleration-time graphs.

Applications of SUVAT

Used to solve constant-acceleration motion problems (e.g., objects speeding up, projectiles with vertical motion).