Physics, asked by Anonymous, 8 months ago

show the derivation of all three equations of motion​

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Answered by Anonymous
1

Answer:

u - initial velocity ; v - final velocity ; S - distance traveled ;

a - acceleration ; t - time taken ;

We can derive three equations of motion using definitions.

acceleration = change in velocity / time taken

acceleration = ( final velocity - initial velocity ) / time taken

a = ( v - u ) / t

a t = v - u

u + a t = v

v = u + a t

distance traveled = average velocity * time taken

distance traveled = ( ( initial velocity + final velocity ) / 2 ) * time taken

S = ( ( u + v ) / 2 ) * t

From 1. v = u + a t

S = ( ( u + ( u + a t ) ) / 2 ) *t

S = ( ( 2 u + a t ) / 2 ) * t

S = ( ( 2 u / 2 ) + ( a t / 2 ) ) * t

S = ( u + a t / 2 ) * t

S = u t + ( a t^2 ) / 2

2. S = u t + ( a t^2 ) / 2

distance traveled = average velocity * time taken

distance traveled = ( ( initial velocity + final velocity ) / 2 ) * time taken

S = ( ( u + v ) / 2 ) * t

From 1. v = u + a t

v - u = a t

( v - u ) / a = t

t = ( v - u ) / a

S = ( ( u + v ) / 2 ) * ( ( v - u ) / a )

S = ( ( v + u ) / 2 ) * ( ( v - u ) / a )

S = ( ( v + u ) * ( v - u ) ) / 2 a

S = ( v^2 - u ^2 ) / 2 a

2 a S = v^2 - u^2

u^2 + 2 a S = v^2

3. v^2 = u^2 + 2 a S

Thus, all the three equations of motion can be derived by definitions.

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Answered by Anonymous
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