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MathidiaMathematics Academy
Kinematics in one dimension
Lesson 64 of 75
Challenge

Vertical motion

Objective. Model motion under gravity and interpret turning points.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Vertical motion under gravity is modelled using the SUVAT equations with constant acceleration g≈9.8m/s², taking upward or downward as positive consistently throughout. At the highest point of an object's flight, its vertical velocity is zero, which is used to find maximum height or time to reach it. For example, a ball thrown upward at 14m/s reaches its highest point when v=0, found from v=u+at as 0=14−9.8t. Always decide the positive direction first, making gravity negative if up is positive, or positive if down is positive.

Worked example

A ball is thrown vertically upward at 19.6m/s. Taking g=9.8m/s², find the time taken to reach maximum vertical height.

6m/s
Illustrated card showing 6m/s
  1. 1At maximum height, vertical velocity v=0
  2. 2Use v=u+at with up positive, so a=−9.8
  3. 30=19.6−9.8t
  4. 4t=2s

Answer: 2 seconds

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Common mistake. Students forget that velocity equals zero at the highest point, instead assuming displacement is zero there. Always use v=0 to find the time or height of a turning point in vertical motion, not s=0.

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