the area bounded by acceleration- displacement curve and displacement axis for the body gives
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As we know that rate of change of velocity is acceleration and we have represented that in calculus form.
a = dv/dt.
Now multiplying both the sides and dividing by dx what we get as shown in the expression below.
a = (dx/dt) x (dv/dx) = v (dv/dx)
After the cross multiplication integration of a into DX is equal to integration of V into DB in the left inside you can see the trapezium that is the area under the acceleration distance curve and on the right hand side you can see the work done that is where was the final velocity and use the initial velocity.
integration (a.dx) = integration (v.dv)
(v^2)/2 which reduces to [ 1/2 (v^2 - u^2)] -> RHS
a = dv/dt.
Now multiplying both the sides and dividing by dx what we get as shown in the expression below.
a = (dx/dt) x (dv/dx) = v (dv/dx)
After the cross multiplication integration of a into DX is equal to integration of V into DB in the left inside you can see the trapezium that is the area under the acceleration distance curve and on the right hand side you can see the work done that is where was the final velocity and use the initial velocity.
integration (a.dx) = integration (v.dv)
(v^2)/2 which reduces to [ 1/2 (v^2 - u^2)] -> RHS
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