Kinematics Eq: Can F Be Changing?

[fball558]

Quick question??

Homework Statement

this is not really a problem just was wondering,
does the following Kenimatics equation only work when the
force is a constant or can i work when the F is changing?
the equation is the one relating acceleration to velocity as follows

V(final)^2 = V(inital)^2 + 2*a*d

i know you can find a by using F=ma
i used this problem a earlier to find final velocity of an orbiting planet.
i used F to be equal to the graviational attraction between the two objects
the whole

G* m1*m2/r^2 thing.

but not sure if that would work or not.
if you know or have an opinion let me know
thanks

 

[swraman]

Yes, that equation is derived under the assumption of constant acceleration, thus constant force.

If you want to find equations of motion for non-constant acceleration, you must start with F=ma and use calculus to solve for the desired quantity.

 

[nlightner]

The kinematics equation V(final)^2 = V(initial)^2 + 2*a*d can still be used even when the force (F) is changing. This equation relates the final velocity (V(final)) to the initial velocity (V(initial)), acceleration (a), and displacement (d). The force (F) can affect the acceleration (a), but it does not have to be constant for this equation to be valid. In your example, you used the gravitational attraction between two objects as the force (F), which can change as the distance (r) between the objects changes. This does not affect the validity of the kinematics equation. However, it is important to note that this equation only works for motion in a straight line with constant acceleration. In more complex situations, such as orbiting bodies, other equations and principles must be used to accurately describe the motion.