FIGURE EX$6.20$shows the velocity graph of a $75$kg passenger in an elevator. What is the passenger’s weight

a. At $1$s?

b. At $5$s?

c. At $9$s?

Weight of an object is the gravitational force exerted on it and it is the product of the mass of the object m and the gravitational acceleration g.

$$\begin{gathered} w=mg \\ w=75kg(9.80m/s^2) \\ w=735N \end{gathered}$$

The equation for the apparent weight of the passenger is

$w_{app}=w(1+\frac{a}{g})$

Here, a is acceleration of the passenger.

The expression which relates acceleration, velocity and time is

$a=\frac{v_f-v_i}{t_f-t_i}$

The acceleration of passengers between time $t=0stot=2s$is

role="math" localid="1647603619704" $a=\frac{v_f-v_i}{t_f-t_i}$

Substitute,

role="math" localid="1647603629913" $$\begin{gathered} v_f=8m/s \\ {v}_i=0m/s \\ {t}_f=2s \\ {t}_i=0s \end{gathered}$$

$$\begin{gathered} a=\frac{v_f-v_i}{t_f-t_i} \\ a=\frac{8m/s-0m/s}{2s-0s} \\ a=4m/s^2 \end{gathered}$$

$$\begin{gathered} w_{app}=735N(1+\frac{4m/s^2}{9.80m/s^2}) \\ {w}_{app}=1035N \end{gathered}$$

The acceleration of passenger at $t=5s$is zero.

The equation for apparent weight of the passenger at time $t=5s$is

$$\begin{gathered} w_{app}=735N(1+\frac{0m/s^2}{9.80m/s^2}) \\ {W}_{app}=735N \end{gathered}$$

The acceleration of passenger at $t=7stot=10s$is $-2m/s^2$

The equation for apparent weight of the passenger at time $t=9s$

$$\begin{gathered} w_{app}=735N(1-\frac{2m/s^2}{9.8m/s^2}) \\ {w}_{app}=585N \end{gathered}$$