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A particle moves along a straight line A...

A particle moves along a straight line AB with constant acceleration. Its velocities are u and v at A and B, respectively. Show that its velocity at the mid-point of AB is `sqrt((u^2 + v^2)/(2))`.

Text Solution

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Let C = mid-point and `v_1` = velocity at .C.
`AC = CB = S/2`
For `AC,v_1^2 = u^2 = 2a s/2" " ...(i)`
and for `CB, v^2 = v_1^2 = 2a s/2 " " ....(ii)`
Use Eqs. (i) and (ii).
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