In the figures given below, find x and y.
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This page is intended for high school or middle school students. For younger students, a simpler explanation of the information on this page is available on the Kids Page. For college students there is another version.
Computer Drawing of a fighter plane with the math equations
for Newton's Second Law of Motion
Sir Isaac Newton first presented his three laws of motion in the "Principia Mathematica Philosophiae Naturalis" in 1686. His second law defines a force to be equal to the change in momentum with a change in time. Momentum is defined to be the mass m of an object times its velocity V.
Let us assume that we have an airplane at a point "0" defined by its location X0 and time t0. The airplane has a mass m0 and travels at velocity V0. The airplane is subjected to an external force F and moves to a point "1", which is described by a new location X1 and time t1. The mass and velocity of the airplane change during the flight to values m1 and V1. Newton's second law can help us determine the new values of V1 and m1, if we know how big the force F is. Let us just take the difference between the conditions at point "1" and the conditions at point "0".
F = (m1 * V1 - m0 * V0) / (t1 - t0)
Newton's second law talks about changes in momentum (m * V) so, at this point, we can't separate out how much the mass changed and how much the velocity changed. We only know how much product (m * V) changed.
Let us assume that the mass stays a constant value equal to m. This assumption is pretty good for an airplane, the only change in mass would be for the fuel burned between point "1" and point "0". The weight of the fuel is probably small relative to the weight of the rest of the airplane, especially if we only look at small changes in time.. If we were discussing the flight of a baseball, then certainly the mass remains a constant. But if we were discussing the flight of a bottle rocket, then the mass does not remain a constant and we can only look at changes in momentum. For a constant mass m, Newton's second law looks like:
F = m * (V1 - V0) / (t1 - t0)
The change in velocity divided by the change in time is the definition of the acceleration a. The second law then reduces to the more familiar product of a mass and an acceleration:
F = m * a