An object with a mass of #5 kg# is traveling at #2 m/s#. If the object is accelerated by a force of #f(x) = x^2 -x +3 # over #x in [1, 9]#, where x is in meters, what is the impulse at #x = 8#?
This is a tricky question, because acceleration is given as a function of x rather the parameter t... In any case write the impulse equation:
So first thing we do it convert this to be in terms of
we have a differential equation of the form:
using chain rule
since the object started with a velocity of 2m/s for
We expect that it was