When Acceleration is Given in Terms of x
If acceleration is a function ofsowe can find the velocity by integration:
and then find the displacement by integrating again
If the acceleration is a function ofwe cannot do this becauseis an unknown function ofWe would have
We can however use the chain rule to express the acceleration as a function of
Now the equationbecomesWe can separate the variables and integrate.
The acceleration of a particle is given in terms ofbyIf the maximum speed of the particle is 10m/s find an expression forin terms of
When the particle moves to the right it accelerates becauseWhen andis max. We can takeand