Henry, whose mass is 95 kg, stands on a bathroom scale in an elevator. The scale reads 830 N for the first 3.0 s after the elevator starts moving, then 930 N for the next 3.0 s. What is the elevator’s velocity 6.0 s after starting?

Henry's mass-$m=95kg$

The scales reads $830N$for the first $3.0s$after the elevator starts moving, then $930N$for the next $3.0s.$

We know that, According to Newton's second law,

$F=ma$

From this; $a=\frac{F}{m}\to eq.1$

Writing equation of motion,

localid="1649614779244" $V_f=v_o+at$$\to eq.2$

substituting $eq.1$in $eq.2$

localid="1649614793717" $V_f=v_o+\frac{F}{m}t\to eq.3$

Now, Before starting $3sec.$assuming $v_0=0$

After starting $3sec.$The net forcelocalid="1649615010224" role="math" $F=830-95\times 9.81=-101.95N$

Therefore, substituting the values of initial velocity and net force on $eq.3$we get

localid="1649615237271" $V_{f,t=3}=\frac{-101.95}{95}\times 3=-3.22\to eq.4$

Now after $3sec.$interval the net force localid="1649615359767" $F=930-95\times 9.81=-1.95N$.

For final velocity after role="math" localid="1649615528476" $6sec.$substitute in eq. 3.

localid="1649615570159" role="math" $V_{f,t=6}=\frac{-1.95}{95}\times 3=-0.06\to eq.5$

Summing $eq.4$and $eq.5$

localid="1649615654824" $$\begin{gathered} V_f=-3.22-0.06 \\ {V}_f=-3.28 \\ {V}_f=-3.3m/s \end{gathered}$$

Velocity containing negative value is downward which means, the elevator is moving down or descending.