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Calculus -Motion - Proof of .


 

In extension questions related to motion, we often need to express acceleration in terms of x (displacement). To prove this equation, follow the following steps:

1. Write down the definition of acceleration:
2. We need to introduce x so split the above definition as a chain rule statement.
3. Notice is the definition of velocity v - so replace that derivative.
4. To obtain v, we can differentiate with respect to v.
5. Now cancel the "dv" terms.