Question

2
3.
Derive the relation: F=ma.​

Answer 1

Question:-

Derive the relation: F=ma.

Solution:-

According to the Newton’s 2nd Law of motion, the rate of change of linear momentum of a body is directly proportional to the applied external force and in the direction of force.

It means that the linear momentum will change faster when a bigger force is applied.

Consider a body of mass ‘m’ moving with velocity v.

The linear momentum of a body is given by:

• p = mv

Now According to Newton’s 2nd Law of Motion:

Force is directly proportional to rate of change of momnetum, that is

$\implies \: F α dp/dt \\ \\ </p><p></p><p> \implies \: F = k dp/dt \\ \\ </p><p></p><p> \implies \: F = k d(mv)/dt \\ \\ </p><p></p><p> \implies \: F = k md(v)/dt \\ \\ </p><p></p><p> \implies \: F = k ma</p><p>$

Experimentally k =1

• F = k ma

Which is the required equation of force.

Answer 2

Step-by-step explanation:

Force is directly proportional to rate of change of momnetum, that is

\begin{gathered}\implies \: F α dp/dt \\ \\ \implies \: F = k dp/dt \\ \\ \implies \: F = k d(mv)/dt \\ \\ \implies \: F = k md(v)/dt \\ \\ \implies \: F = k ma\end{gathered}

⟹Fαdp/dt

⟹F=kdp/dt

⟹F=kd(mv)/dt

⟹F=kmd(v)/dt

⟹F=kma