Brainlag Plus
Brainlag PlusGradient at a point, and the kinematics formulae
Estimate the rate of change at a point on a curve from a tangent, compare it with an average rate from a chord, and (OCR J560) use the kinematics formulae v = u + at, s = ut + ½at² and v² = u² + 2as, which link to the gradient and area of a speed-time graph.
A tangent shows the gradient at one point (Higher)
A curve's steepness changes as you move along it. The gradient at a point is the gradient of the tangent there: the straight line that just touches the curve at that point and has its direction. Draw it with a ruler, then pick two points on the tangent that are far apart, ideally where it crosses grid lines.
- tangent at t = 4 through (2, 4) and (7, 24)
- gradient = (24 − 4) ÷ (7 − 2) = 20 ÷ 5 = 4
- acceleration at t = 4 ≈ 4 m/s²
It is an estimate because the tangent is drawn by eye.
The rest of this lesson and its 10 practice questions are in Plus.
Screen 1 of 4, free to read.
- 10 exam-style questions, marked as you go, each with a worked solution
- Anything you get wrong is saved to your flashcards