2nd law of motion... Derivation?

This statement is expressed in equation form as, a=Fnetm The above equation can be rearranged to a familiar form as F=ma Since force is a vector, Newton’s second law can be written as F⃗ =ma⃗ The equation shows that the direction of the total acceleration vector points in the same direction as the net force vector. Deriving Newton’s Second Law Force is equal to the rate of change of momentum For Changing Mass Let us assume that we have a car at a point (0) defined by location X0 and time t0. The car has a mass m0 and travels with a velocity v0. After being subjected to a force F, the car moves to point 1 which is defined by location X1 and time t1. The mass and velocity of the car change during the travel to values m1 and v1. Newton’s second law helps us determine the new values of m1 and v1 if we know the value of the acting force. Taking the difference between point 1 and point 0, we get an equation for the force acting on the car as follows: F=m1v1−m0v0t1−t0 Let us assume the mass to be constant. This assumption is good for a car because the only change in mass would be 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 car, especially if we only look at small changes in time. Meanwhile, if we were discussing the flight of a bottle rocket, then the mass does not remain constant and we can only look at changes in momentum. For Constant Mass For a constant mass, Newton’s second law can be equated as follows: F=mv1−v0t1−t0 We know that acceleration is defined as the change in velocity divided by the change in time. The second law then reduces to a more familiar form as follows: F=ma The above equation tells us that an object will accelerate if it is subjected to an external force and the amount of force is directly proportional to the acceleration and inversely proportional to the mass of the object. What is a Net Force? A net force ΣF is the sum of all forces acting on a body. More precisely, it is the vector sum of all forces acting on a body. Calculating the net force acting on a horse Consider two forces of magnitude 30 N and 20 N that is exerted to the right and left respectively on the horse shown in the picture. If we assume the rightward direction as positive, then the net force on the horse can be calculated as follows: ∑F=30N−20N=10N ∑F=10Ntotheright

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