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Derive newton\'s 1st law of motion from 2nd law of newton.

Answer» \tFirst Law of Motion: Newton’s first law of motion states that a body at rest will remain at rest, and a body in motion will continue in motion in a straight line with a uniform speed, unless it is compelled by an external force to change its state of rest or of uniform motion.All objects resist a change in their state of motion. The tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called inertia. This is why, the first law of motion is also known as the law of inertia. We tend to remain at rest with respect to the seat until the drives applies a braking force to stop the motorcar. With the application of brakes, the car slows down but our body tends to continue in the same state of motion because of its inertia. A sudden application of brakes may thus cause injury. Safety belts are worn to prevent such accidents as they exert a force on our body to make the forward motion slower. When we are standing in a bus and the bus begins to move suddenly we tend to fall backwards because the sudden start of the bus brings motion to the bus as well as to our feet in contact with the floor of the bus. But the rest of our body opposes this motion because of its inertia.When a motorcar makes a sharp turn at a high speed, we tend to get thrown to one side due to the law of inertia. We tend to continue in our straight-line motion.\xa0\tSecond Law of Motion:The second law of motion states that the rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force.The quantity of motion in a body depends on the product of mass and velocity of the body termed as momentum. The momentum (p) of a body is defined as the product of its mass (m) and velocity (v) and has the same direction as that of the velocity. Its SI unit is kilogram metre per second (kg m s−¹).Momentum = mass × velocityp = m × vMomentum has both magnitude as well as direction; hence it is a vector quantity.Momentum of a body at rest is zero.\xa0\tMathematical Formulation of Second Law of Motion:Suppose an object of mass, m is moving along a straight line with an initial velocity, u. It is uniformly accelerated to velocity, v in time, t by the application of a constant force, F throughout the time, t. The initial and final momentum of the object will be, p1 = mu and p2 = mv respectively.The change in momentum ∝ p2 – p1∝ mv – mu∝ m × (v – u).The rate of change of momentum ∝ m × (v – u)/tOr, the applied force,F ∝ m × (v – u)/tF = km × (v – u)/t = kmaHere, a = [(v – u)/t ] is the acceleration, which is the rate of change of velocity. The quantity, k is a constant of proportionality.The SI unit of mass and acceleration are kg and ms-2.One unit of force is defined as the amount that produces an acceleration of 1 ms-2 in an object of 1 kg mass. 1 unit of force = k × (1 kg) × (1 ms-2).


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