Linear Motion: Graphs of Linear Motion

Distance-Time GraphsPlotting a graph of distance from a given point against time can be useful in illustrating different types of motion

The body starts moving from point A and moves towards point B very quickly The steeper the graph, the higher the slope, and the body is moving faster At point C it has a constant velocity Constant velocity means that the body has no acceleration A horizontal graph indicates that the body is stationary From point D to point E the body is returning to the start

Velocity-Time GraphsWe are interested in graphs that involve a constant acceleration throughout or ones where the acceleration changes instantly from one value to another

The slope is equal to the velocity Slope = (y₂ - y₁)/(x₂ - x₁) = (s₂ - s₁)/(t₂ - t₁) = s/t = v

Time (in seconds) is plotted on the x-axis Distance (in metres) is plotted on the y-axis

Velocity (in metres per second) is plotted on the y-axis Time (in seconds) is plotted on the x-axis

The slope is equal to the acceleration Slope = (y₂ - y₁)/(x₂ - x₁) = (v₂ - v₁)/(t₂ - t₁) = (v - u)/t = a

The area under the graph is equal to the distance travelled Area = area of rectangle + area of triangle

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