BeginnerTopic 22 of 106Engineering Mechanics

Uniform acceleration equations

v=u+at and s=ut+½at² apply for constant acceleration.

In depth

For constant acceleration: v=u+at, s=ut+½at², v²=u²+2as, s=(u+v)t/2. They only apply when a is constant. Free fall near Earth uses a=g.

Key points

  • Choose a sign convention
  • List known and unknown quantities
  • Not valid if a varies
Example

A car braking at 8 m/s² from 20 m/s stops in 20²/(2×8)=25 m.

Why it matters

These equations let you solve constant-acceleration problems quickly, such as braking distance or the time for a drop test.

Where this is used

  • Calculating the stopping distance of a car with constant braking.
  • Finding the speed of a falling object before impact.
  • Estimating the launch speed of a ball from its flight time.

Frequently asked questions

What is Uniform acceleration equations?

v=u+at and s=ut+½at² apply for constant acceleration.

Why is it important to understand uniform acceleration equations?

These equations let you solve constant-acceleration problems quickly, such as braking distance or the time for a drop test.

Can I use these equations when acceleration changes?

No. They apply only to constant acceleration, so split the motion into intervals with constant acceleration or integrate the changing one.

Which equation do I use if time is unknown?

Use the one that relates velocity and displacement without time, v squared equals u squared plus 2as.

How is Uniform acceleration equations used in practice?

Typical applications include calculating the stopping distance of a car with constant braking, finding the speed of a falling object before impact and estimating the launch speed of a ball from its flight time.

What should I learn before Uniform acceleration equations?

Study "Kinematics of a particle" first (topic 21 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.

What are the key points of Uniform acceleration equations?

Choose a sign convention. List known and unknown quantities. Not valid if a varies.

Can you give an example of Uniform acceleration equations?

A car braking at 8 m/s² from 20 m/s stops in 20²/(2×8)=25 m.

What comes after Uniform acceleration equations?

The next topic is "Projectile motion", which builds directly on this one.

How difficult is Uniform acceleration equations?

It is classed as Beginner in Engineering Mechanics (topic 22 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.

Learning path

Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.

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