How Does Impulse Affect the Velocity of a Block?

[teenidle]

Homework Statement

A 2kg block, initially moving due east at 6m/s, is acted upon by an impulse having magnitude 4Ns and direction due west. What is the final velocity of the block?
a) 8m/s west
b) 4m/s west
c) 4m/s east
d) 8m/s east

Homework Equations

change in momentum = F*(time interval) = mass*Velocity(final) - mass*velocity(initial)

The Attempt at a Solution

assuming west is the (-) direction
4Ns = (2kg)(-Vf) - (2kg)(6m/s)
2Ns = (-Vf -6m/s)
-8m/s = Vf
so 8m/s west

 

[G01]

You have the right idea, but I think you are making a sign error.

Your relevant equation is correct, so start with that.

Now, the impulse is directed west, so it should be negative based on your sign convention. Also, I don't know why you multiplied v_f by a negative sign in your first line of work. That is changing your answer. What do you get now that you take those sign errors into account?

 

[ogb p]

I would like to clarify that the answer is not necessarily 8m/s west. The calculation provided is correct, but the answer would depend on the reference frame used. If we consider the initial velocity of the block as the reference frame, then the final velocity would be 8m/s east. However, if we consider the external frame of reference, then the final velocity would be 8m/s west. It is important to specify the reference frame when discussing momentum and velocity.