The Uniform Acceleration Equations
Using v = u + at and v squared = u squared + 2as when acceleration is steady, including picking which one fits the quantities given. The graph work becomes algebra that answers questions no graph was drawn for.
What a learner can do afterwards
- Lists the known and wanted quantities of a problem and picks the equation that links them
- Rearranges each equation to make any one of its quantities the subject
- Uses a negative acceleration for a braking or rising object and reads the sign of the answer correctly
1 · Read
When acceleration stays steady, use v equals u plus a t. Here u is the starting velocity, v is the final velocity, a is the acceleration and t is the time. Know three and find the fourth: to find time, write t equals v minus u over a.
When time is missing but distance s is known, reach for v squared equals u squared plus 2 a s. It links starting speed, final speed, acceleration and distance with no t in sight. Working out a falling stone's speed from its drop is this kind of question.
Suppose a car goes from 0 to 20 metres per second in 10 seconds, speeding up steadily. Average acceleration is the speed change divided by the time: 20 minus 0 over 10 is 2 metres per second squared. That is v equals u plus a t rearranged to solve for a.
List what you know and what you want before picking. If time is missing, use the second equation; if distance is missing, use the first. Keep signs honest: braking takes negative acceleration if forward is positive, and a ball thrown up has negative acceleration while still rising.
List knowns, pick the equation that fits, and keep the signs honest.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.