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,