Question:
How do I calculate the velocity of an object on which multiple forces are acting, at any given moment (in a 2D space)? The forces could have been applied at different moments.
The Problem:
I have an object on which multiple forces are acting at the same time. I have thought of these forces as vectors with a magnitude (in N) and an angle (in Deg).
I have already figured out how to get the resultant vector with the right magnitude and angle. With this, I could calculate the object's acceleration, using Newton's 2nd law: $F = ma$
To get the velocity at any given time, I need to get the time since the force was applied and use it in the formula: $v = at$. But what happens when two forces get applied at different times? What should I use for $t$? I already know the result acceleration and angle, but just don't know what to use for $t$.
Example: An object in 2D space, which has a mass of $1 kg$, is moving to the right with an acceleration of $5m/s^2$, after 3 seconds, it is moving to the right with a velocity of $15 m/s$. Then, it gets pushed with a force of $10 N$ from the bottom, which gives it an acceleration of $10m/s^2$ towards the top. What would be the velocity of the object 10 seconds later?
Best Answer
Here is the outline of what you can do: a constant net force of $F_t$ acts on an object of mass $m$ between time $t$ and $t'$. If the object's velocity is $v_t$ at time $t$, then its velocity at time $t'$ is
$$v_{t'}=v_t+(F_t/m)(t'-t).$$
This becomes the initial velocity at time $t'$ at which a new constant net force $F_{t'}$ is applied and you just rinse and repeat.