# Episode 206: Uniform and non-uniform acceleration

Lesson for 16-19

- Activity time 90 minutes
- Level Advanced

This episode continues to look at basic kinematics and introduces the equations of motion for uniform acceleration. This involves a little calculation practice.

Lesson Summary

- Demonstration (or student experiment): Non-uniform acceleration (20 minutes)
- Discussion: Developing equations of motion (10 minutes)
- Student experiment: Measuring acceleration due to gravity
*g*(20 minutes) - Student questions: Calculations (30 minutes)
- Worked example: Average velocity (10 minutes)

Uniform acceleration is compared with non-uniform acceleration.

## Demonstration (or student experiment): Non-uniform acceleration

Students will have already considered uniformly accelerated motion. This demonstration (or experiment) uses a similar method to consider non-uniform motion. You can conclude the demonstration by discussing the relationships shown on the graphs, stressing that these hold for both uniform and non-uniform motion.

Episode 206-1: An experimental velocity-time graph (Word, 35 KB)

## Discussion: Developing equations of motion

Here you can develop the equations of motion (the SUVAT equations

).

Confident mathematicians will enjoy the mild challenge of developing SUVAT equations whereas weaker or non-mathematical students may find the activity surprisingly difficult. It is therefore best to proceed through the activity at a reasonable pace so that you concentrate on the results and using the SUVAT equations.

Episode 206-2: Deriving the equations of motion (Word, 41 KB)

## Student experiment: Measuring acceleration due to gravity g

Measuring the acceleration due to gravity g is a nice, simple experiment that also brings up the concepts of precision and accuracy. Of course, the students will know

the value of *g*, and may well have measured it. Nonetheless, it is a useful exercise to build good experimental practice.

Episode 206-3: Measuring the acceleration of free fall (Word, 21 KB)

## Student questions: Calculations

These are a few simple questions that go over the ideas met in the unit. They include practice with interpreting motion graphs.

Episode 206-4: Motion under gravity (Word, 38 KB)

Episode 206-5: Thrust SSC (Word, 67 KB)

## Worked examples: Average velocity

You might like to use the question below to highlight that the equations of motion (SUVAT equations) only apply to uniform acceleration.

A cyclist travels a displacement of 300 m due North at a velocity of 10 m s^{-1}. She travels the next 300 m in the same direction at a velocity of 15 m s^{-1}. Calculate the average velocity of the cyclist.

Answer: First 300 m takes:

300 m10 m s^{-1} = 30 s

Second 300 m takes:

300 m15 m s^{-1} = 20 s

average velocity = total displacementtotal time

average velocity = 600 m50 s

*v*_{average} = 12 m s^{-1}

Many weaker pupils will assume the answer is 12.5 m s^{-1} . You will have to explain why the equation:

average velocity = *v*+*u*2

cannot be used in this example. The equation only applies to uniformly accelerated motion. The cyclist spends longer travelling at 12 m s^{-1} than at 15 m s^{-1} .