lift performs the first part of ascent with uniform acceleration a and the remainder with uniform retardation $$2a$$. The lift starts from rest and finally comes to rest. If t is the time of ascent. Find the height ascended by lift.

Question

Infinity Learn · Accepted Answer

Let OAB be the $$velocity-time$$ graph of the lift. The ordinate at A (i$$.e., $$AM) represents maximum velocity.Total distance travelled $$=$$ Area of the  ΔOAB $$=$$ $$12$$×OB×AMAM $$=$$ v, OM $$=$$ $$t1$$, $$t1+t2=$$ OB $$=$$ t, MB $$=$$ $$t2$$ ∴    ΔOAB $$=$$ $$12$$×tv $$=$$ hOr vt $$=$$ $$2h$$   ..(i)Now$$  $$vt1$$ $$=$$ a  or  $$t1$$ $$=$$ va   .....$$(ii)and$$  $$vt2$$ $$=$$ $$2a$$  or  $$t2$$ $$=$$ $$v2a$$   .....$$(iii)Adding$$ $$(ii) and $$(iii)t$$ $$=$$ $$t1+t2$$ $$=$$ $$va+v2a$$ $$=$$ $$3v2a$$ $$=$$ $$32a$$×$$2htor$$  $$at2$$ $$=$$ $$3h$$   ⇒ h $$=$$ $$at23$$

lift performs the first part of ascent with uniform acceleration a and the remainder with uniform retardation 2a. The lift starts from rest and finally comes to rest. If t is the time of ascent. Find the height ascended by lift.

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