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Initial speed $$v_{\text{initial}} = k \space \text{m/s}$$ in the positive x-direction $$\hat{i}$$
Applied force $$\mathbf{F} = n \, \text{N} $$ in the positive y-direction $$\hat{j}$$
$$ Mass = m \space \text{kg} $$
If this force is applied to the particle, I feel that the resultant velocity would have both i and j components, and so speed cannot remain constant
but since the force is perpendicular and no work is done, speed cannot change. I would like to see this solution work out vectorally so I see where I'm going wrong.
$\begingroup$If this force is constantly applied then obviously it will stop being perpendicular and then the speed can change. You need a force that is perpendicular to the velocity at all times for the speed to stay constant.$\endgroup$
$\begingroup$You mean for one instant? Are you sure it is a finite force and not infinite force, i.e. a one-instant finite impulse? Forces are such things that "one time" does not make sense for them.$\endgroup$
$\begingroup$I could be wrong here, just trying to understand how this would work. What is the right way to think about this then? adding a force along the y axis to a particle moving along the x axis with speed v_x should result in v_x + something*v_y (since the force is along the y axis) which means the kinetic energy should change since speed now has two components but since W = FdCos(theta) and the angle is 90, W is zero and the kinetic energy should remain constant Im trying to reconcile these two ideas$\endgroup$
