The second law of motion,
also known as Newton's second law of motion, states that the force acting on an
object is directly proportional to the acceleration of the object.
This can be expressed
mathematically as:
F
= ma
Where F is the force
acting on the object, m is the mass of the object, and ‘a’ is the acceleration
of the object.
To prove this law
mathematically, we can use the following steps:
Assume that the object
has a mass of m and is subjected to a force F.
Assume that the object
experiences acceleration ‘a’ due to the force F.
Use the definition of
acceleration, which is the rate of change of velocity, to express the
acceleration as a = (v - u) / t, where v is the final velocity, u is the
initial velocity, and t is the time taken.
Use the definition of
force, which is the rate of change of momentum, to express the force as F = (mv
- mu) / t, where mv is the final momentum, and mu is the initial momentum.
Substitute the expression
for acceleration (a) and force (F) into the equation F = ma, and simplify:
F
= ma
(mv
- mu) / t = m(v - u) / t
mv
- mu = ma t
F
= ma
Therefore, the equation F
= ma holds true, proving the second law of motion mathematically.
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