The friction coefficient between the blocks is `mu`. Sketch a graph showing variation of acceleration of the blocks will move separately.

Explanation

(a) If `kt le mu m_(1) g` , the blocks will move together as a single block.
`kt = (m_(1) + m_(2)) a_(0) rArr a_(0) = (k)/(m_(1) + m_(2)) t`
(`a v//s t` graph will be straight line of slope `(k)/(m_(1) + m_(2))`)
If `kt ge mu m_(1) g`, the blocks will move separately
`kt - mu m_(1) g = m_(1) a_(1) = (kt)/(m_(1)) - mu g`
(`a_(1) v//s t` graph will be straight line of slope `(k)/(m_(1))` and negative intercept)
`mu m_(1) g = m_(2) a_(2) rarr a_(2) = (mu m_(1) g)/(m_(2))`
(`a_(2) v//s t` graph will be straight line parallel to the `t`- axis )
At ` t = t_(0)`, the blocks will move separately
`a_(0) = a_(1)`
`(k)/(m_(1) + m_(2)) t_(0) = (k)/(m_(1)) t_(0) - mu g`
`k t_(0) [ (1)/(m_(1)) - (1)/((m_(1) + m_(2)))] = mu g rArr t_(0) = ((m_(1) + m_(2))m_(1) mu g)/(m_(2) k)`