A lift car starts at ground level $O$ and moves vertically in a test shaft. Its displacement above

Question

A lift car starts at ground level $O$ and moves vertically in a test shaft. Its displacement above $O$, $s$ metres, after $t$ seconds is $s=4t^2-\dfrac23t^3$, for $0\leq t\leq6$. (i) Find the velocity of the lift at time $t$. (ii) Find the greatest height reached by the lift. (iii) Show that the lift returns to ground level at $t=6$, and find the total distance travelled in the $6$ seconds.

Accepted Answer

(i) $v=2t(4-t)\text{ m s}^{-1}$; (ii) $\dfrac{64}{3}\text{ m}$; (iii) $\dfrac{128}{3}\text{ m}$

Lift rises and returns to ground level

Lift rises and returns to ground level

Solution:

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