Write mathematical form of Newton's second law of motion.
Write mathematical form of Newton's second law of motion.
The correct option is (B) F=ma.
Consider an object of mass m, moving along a straight line with an initial velocity u. Let us say, after a certain time t, with a constant acceleration, the final velocity becomes v. Here we see that, the initial momentum
p1=mu
The final momentum
p2=mv
The change in momentum can be written as
p2−p1=mv−mu=m(v−u)
As we know, the rate of change of momentum with respect to time is proportional to the applied force.
Therefore the applied force F∝m(v−u)t
or F∝ma (Since v−ut=a)
or F=kma
where k is the constant of proportionality whose value is 1.
Therefore, F=ma.
The second law of motion gives us a method to measure the force acting on an object as a product of the mass of the object and the acceleration of the object which is the change in velocity with respect to time.
The correct option is (B) F=ma.
Consider an object of mass m, moving along a straight line with an initial velocity u. Let us say, after a certain time t, with a constant acceleration, the final velocity becomes v. Here we see that, the initial momentum
p1=mu
The final momentum
p2=mv
The change in momentum can be written as
p2−p1=mv−mu=m(v−u)
As we know, the rate of change of momentum with respect to time is proportional to the applied force.
Therefore the applied force F∝m(v−u)t
or F∝ma (Since v−ut=a)
or F=kma
where k is the constant of proportionality whose value is 1.
Therefore, F=ma.
The second law of motion gives us a method to measure the force acting on an object as a product of the mass of the object and the acceleration of the object which is the change in velocity with respect to time.
