Question

Derive the formula F=ma

Answer 1

HOLA

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According to 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 the force.

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

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

The continuing or 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

F α dp/dt

F  = k dp/dt

F = k d(mv)/dt

F = k md(v)/dt

F = k ma

Experimentally k =1

F = k ma

Which is the required equation of force. 

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HOPE MY ANSWER HELPED U !!

Answer 2

Heya friend,

If a body of mass "m" moving at initial velocity "u" accelerates uniformly with an acceleration "a" for time"t" so that it's final velocity changes Into "v".
then initial momentum p1 = mu
final momentum p2 = mv

change in momentum = p1-p2
= mv-mu
= m(v-u)
according to 2nd law of motion
F = change in momentum ÷ time

F = p2-p1 ÷ t

F = m(v-u)÷ t

F = ma 《 v- u ÷ t 》

hence derived...


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