Can these equations of motion be used in a situation when the acceleration varies with time? can they be used when the acceleration is zero?
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Can the equation of motion be used in a situation where acceleration varies with time? Can they be used when acceleration is zero?
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The term “equations of motion” is very generic - they’re really just any ordinary differential equation that model the motion of a specific dynamical system. Its solution is the position of the body vs. time. There’s no restriction as to whether the acceleration is constant or time-variable, it all depends on the nature of the forces acting on the body. Two examples where acceleration varies as a function of time: 1) a drag-gravity model and 2) a spring-mass-damper system. These forces aren’t constant, so the accelerations won’t be either.
The equation for the first one looks something along the lines of:
mx′′−A(x′)2+B/(x+R)2=0
where A and B are constants, and R is the radius of the “pulling body.”
The equation of the second one is:
mx′′+cx′+kx=0
where k is the spring constant and c is the damping coefficient.
You can also find an equation of motion for when acceleration is zero, which corresponds to a net force of zero, but that’s not a very interesting equation of motion. In fact, there’s practically nothing to it.
when a=0 m/s²
then there are two situations they are
1) uniform velocity
2) body is at rest
for 1st situation
we can use
v=u+at
v²-u²=2as
for 2nd situation
S=0
it can't travel because whole value will be zero