Movement & Position - Edexcel IGCSE Physics

Distance-Time Graphs

• A distance-time graph shows how distance from a starting position varies over time for motion in a straight line.

• Constant speed: straight line; slope represents speed magnitude.

• Steeper slope = larger speed; shallower slope = smaller speed.

• Horizontal line (slope 0) = stationary.

• Changing speed is shown by a curved line; increasing slope = accelerating, decreasing slope = decelerating.

• Plotting distance-time graphs is a key skill; practice plotting and interpretation.

Speed from Distance-Time Graphs

• Speed is the gradient of the distance-time graph: $v = \frac{\Delta y}{\Delta x}$ where $\Delta y$ is distance and $\Delta x$ is time.

• Units: distance in metres, time in seconds, speed in m/s.

Average Speed

• When speed varies, use average speed to describe overall rate: $\text{average speed} = \frac{\text{distance moved}}{\text{time taken}}$

Formula Triangles and Rearranging Equations

• Formula triangles help rearrange equations quickly; for more complex equations (e.g., $v^2 = u^2 + 2 a s$) you may need manual rearrangement.

• To use triangles: cover up the quantity to calculate to reveal the rest.

Core Practical: Investigating Motion (Overview)

• Aim: investigate motion by measuring speed via distance moved and time taken.

• Independent variable: distance (d); Dependent variable: time (t).

• Control variables: use the same object for measurements.

• Equipment: ruler (≈1 mm), stopwatch (≈0.01 s), tape measure/metre rule.

• Note: Light gates can be used for more precise timing.

Acceleration

• Acceleration = rate of change of velocity: $a = \frac{\Delta v}{t}$

• Where $\Delta v = v - u$ (final velocity minus initial velocity).

• So: $a = \frac{v - u}{t}$

• Positive acceleration = speeding up; negative acceleration = slowing down (deceleration).

• Units: $\text{m/s}^{\text{2}}$

Velocity-Time Graphs

• A velocity-time graph plots velocity against time.

• Positive gradient = increasing velocity (acceleration); negative gradient = decreasing velocity (deceleration).

• A straight line with non-zero gradient indicates constant acceleration; the gradient magnitude equals the acceleration.

• Horizontal line (gradient = 0) = constant velocity.

• Acceleration from a velocity-time graph: $a = \frac{\Delta y}{\Delta x}$ where $\Delta y$ is velocity and $\Delta x$ is time.

Gradient on Velocity-Time Graph

• To find the gradient, identify the section and compute: $a = \frac{\Delta v}{\Delta t}$

Area Under a Velocity-Time Graph

• Area under a velocity-time graph = displacement (distance travelled).

• If a section forms a triangle (accelerating/decelerating): $\text{Area} = \tfrac{1}{2} \text{base} \times \text{height}$

• If a section forms a rectangle (constant velocity): $\text{Area} = \text{base} \times \text{height}$

• Total distance travelled = sum of all enclosed areas under the graph over the given time interval.

Area Examples (General Approach)

• Break the graph into triangles and rectangles; compute each area and add.

• The total area under the line between the start and end times gives the total distance travelled.

Uniform Acceleration

• Uniform (constant) acceleration: use the equation $v^2 = u^2 + 2 a s$

• Variables: $v$ = final speed, $u$ = initial speed, $a$ = acceleration, $s$ = distance moved (along the path).

• Useful when time is not specified.

• Tips for rearranging: apply opposite operations to both sides and show working; triangles are helpful but not always sufficient.