Question

Derive:

$\mathtt{v^{2} = 2aS}$​

Answer 1

We know that, a = dv/dt

=> a = dv/dx × dx/dt

=> a = dv/dx . v

=> v.dv = a.dx

Integrate the above expression under the limit u--»v

=> Int. (v.dv) = Int. (a.dx)

=> int. (v.dv) = a {int.(dx)}

=>| (v^2)/2 | u-»v = a|x| 0-»s

=> (v^2 - u^2)/2 = a(s - 0)

=> v^2 - u^2 = 2as

=> v^2 = u^2 + 2as

Note:-

I have used int. for the sigh of integration.

Now, when u = 0, i.e., initial velocity is zero then,

v^2 = 0 + 2as

[v^2 = 2as]

Answer 2

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