If acceleration is a function of
so
we can find the velocity by integration:
and then find the displacement by integrating again
If the acceleration is a function of
we cannot do this becauseis an unknown function of
We would have
We can however use the chain rule to express the acceleration as a function of
Now the equation
becomes
We can separate the variables and integrate.
Example
The acceleration of a particle is given in terms of
by
If the maximum speed of the particle is 10m/s find an expression forin terms of
When the particle moves to the right it accelerates because
When
andis max. We can take
and
