Video Transcript
Complete the following equation: ๐
equals d by d๐ก of mass times what.
When we think about equations that
describe forces acting on a body, we tend to think about Newtonโs second law of
motion for constant mass. The magnitude of the acceleration
of a body depends on the magnitude of a force and the mass of the body. And the formula we use is ๐
equals
๐๐. However, we can also think about
Newtonโs second law of motion in terms of the rate of change of the momentum of the
body. That is, force is equal to the
derivative of momentum with respect to time.
But of course, the momentum of a
body is given by ๐๐ฃ, where ๐ is its mass and ๐ฃ is its velocity. So we can, alternatively, calculate
the force by finding the derivative of mass times velocity with respect to time. And with that in mind, we can now
complete the equation in our question ๐
is d by d๐ก of mass times what. Well, we know itโs the derivative
with respect to time of ๐๐ฃ, of mass times velocity. And so the missing word is
velocity.
