Lift Question

[wildareal]

In a tall building the lift passes the 50th floor with a velocity of -8m/s and an acceleration of 1/9(t-5)m/s^2. If each floor spans a distance of 6m, find at which floor the lift will stop.

[Martoman]

t = 0, v = -8

c = -8

We want to know where the lift stops, ie when its final velocity is 0 so:

v = 0,







t = 18 only as t cannot equal a negative number ie -8

So you want to find the total distance covered between t = 0, 18

This is the integral of the velocity function but we need to check by graphing if any negative areas will muck us up.

A graph shows its below the x axis for the interval [0,18] (lovely) so we just take the integral then the negative of it or change the signs



Now each floor spans 6 meters so 126/6 = 21

assuming its going down then 50-21 = 29th floor.