# 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#?

##### 1 Answer

#### Answer:

#### Explanation:

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:

Let

using chain rule

but

since the object started with a velocity of 2m/s for

We expect that it was