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## Chapter 7. Equations of motion (part 1): Playing With Equations

It’s time to take things to another level.

So far, you’ve done experiments, drawn graphs of their results and worked out equations from them. But there’s only so far you can go, since sometimes your graph isn’t a straight line. In this chapter, you’ll expand your math skills by making substitutions to work out a key equation of motion for a curved displacement - time graph of a falling object. And you’ll also learn that checking your GUT reaction to an answer can be a good thing.

## How high should the crane be?

The Dingo wants to invite the Emu to his birthday party - but the only way he’ll get him to stay still for long enough is by catching him in a cage!

In Chapter 6, you figured out that it takes the Emu 2.0 s to get from the corner to the target on the road while running at his constant speed.

You also figured out that the cage’s velocity after 2.0 s won’t lead to it shattering on impact, by drawing its velocity - time graph and working out the equation .

But the Dingo wants to know how high to set the crane. Which means that you now need to work out the cage’s displacement after it’s been falling for 2.0 s.