Question

prove that:force=mass*accelaration

Answer 1

prove that:force = mass * acceleration

Answer

Newton's $2^{\mathrm{nd}}$ law of motion states that the net force acting on a system is directly proportional to rate of change of momentum of the system. We can write, $\vec{F} = \frac{d\vec{p}}{dt}$ where, $\mathfrak{p}$ is the momentum. Now we have, momentum, $\vec{p} = m\vec{v}$ where, $\mathfrak{m}$ is mass and $\mathbf{v}$ is the velocity. Hence $\vec{F} = m\frac{d\vec{v}}{dt}$. Now, acceleration is defined as the rate of change of velocity, $\vec{a} = \frac{d\vec{v}}{dt}$. Thus, $\vec{F} = m\frac{d\vec{v}}{dt} = m\vec{a}$ or Force = mass * acceleration.