Calculating Time of Force Application in Non-Uniform Motion

[neoking77]

A 230N force causes a 4.0kg to accelerate from 5.0m/s North to 3.0m/s east. for how much time does hte force act?

t = m(vf-vi) / F

i got this but the trouble is vf and vi are in different directions...and since t is not a vector i can't break it down to components. what should i do?

 

[Psi-String]

Maybe you can do it by this way.
let $$\vec{v_i} =(0,5)$$ $$\vec{v_f}=(3,0)$$
so $$\Delta \vec{v} =(3,-5)$$

 

[Tide]

You can integrate

$$\frac{d\vec{v}}{dt} = \frac{\vec{F}}{m}$$

Your solution will be two equations (one for each component of velocity). You know the initial and final velocity vectors. Your unknowns are the two components of $\vec F$ and t but you also know

$$F^2 = F_x^2 + F_y^2$$

where F = 230 N. You should be able to handle the details.

 

[andrevdh]

using
$$F_x\Delta t\ =\ m\Delta v_x\ =\ a$$
$$F_y\Delta t\ =\ m\Delta v_y\ =\ b$$
and then
$$a^2\ +\ b^2\ =\ \Delta t^2 \mid F\mid^2$$