Video Transcript
Complete the following equation: 𝐅
equals d by d𝑡 of mass times what.
When we think about equations that
describe forces acting on a body, we tend to think about Newton’s 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 𝐅 equals
𝑚𝑎. However, we can also think about
Newton’s 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 𝑚𝑣, where 𝑚 is its mass and 𝑣 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 𝐅 is d by d𝑡 of mass times what. Well, we know it’s the derivative
with respect to time of 𝑚𝑣, of mass times velocity. And so the missing word is
velocity.
