Question

Derive the equation F = m x a

Answer 1

Derivation:-

Consider a body of mass "m" moving with velocity "V" under the action of net external force "F" in the direction of velocity.

---->If its velocity increases by dv in time intervals dt.

F is directly proportional to $\frac{dp}{dt}$

F = K $\frac{dp}{dt}$

F=K $\frac{d}{dt}$ mv (P=mv)

F =K [m $\frac{dv}{dt}$ + V $\frac{dm}{dt}$ ]

F= K [ma+0]

Here,

K=1

so,

F=ma

Know More:-

We know that F=ma is Newtons second law.

Newtons second law:-

• The rate of change of a body is directly proportional to the resultant external force acting on the body and takes place in the direction in which the force acts.