2.8 Gradient of a Distance-Time Graph
The gradient is the measure of the slope of a line.
Consider the distance-time graph of uniform speed again. Select any two values of time, t₁ and t₂. Draw two vertical dotted lines at t₁ and t₂ on the x-axis. These lines meet the graph at points P and Q. From these points, draw horizontal lines to meet the y-axis at S₁ and S₂ respectively.
Distance covered in this time interval is:
S₂ − S₁ = S
Time taken is:
t₂ − t₁ = t
The slope or gradient of the graph is the measure of tangent θ of the triangle RPQ:
Slope = RQ / PR
Slope = (S₂ − S₁) / (t₂ − t₁) = S / t
From the equation of speed, S/t = v_av, the average speed during the time interval t.
Therefore:
lightbulbGradient of the distance-time graph is equal to the average speed of the body.