# An object with a mass of #5 kg# is traveling at #6 m/s#. If the object is accelerated by a force of #f(x) = 2x^2-x# over #x in [0, 9]#, where x is in meters, what is the impulse at #x = 3#?

##### 2 Answers

let's write the impulse equation:

we have a differential equation of the form:

Let

using chain rule

Note now the Force function is a function of x ONLY.

The velocity after replacing u by v is:

evaluate C by setting v(0) = 6

now calculate v(3)

let's write the impulse equation:

we have a differential equation of the form:

Let

using chain rule

Note now the Force function is a function of x ONLY.

since the object started with a velocity of 6m/s

now calculate v(3) = 8.323 m/s

And the Impulse,