GB-24-08-001 · Gradient of a curve

A tangent to a distance–time curve passes through (1, 7) and (7, 19). Time is in seconds and distance is in metres. Use the tangent to estimate the speed at the point of contact.

Gradient of a Curve (Tangent Method) Application of related method — Booklet p. 58 & p. 80

Method

1) Pick two points (x₁, y₁) and (x₂, y₂) on the tangent

2) Calculate gradient m = (y₂ − y₁) / (x₂ − x₁)

Worked Example (GB-24-08-001)

x_1 \quad y_1

(1,\; 7)

and

x_2 \quad y_2

(7,\; 19)

m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{19 - (7)}{7 - (1)} = \frac{12}{6}

2 m/s