$A$ woman starts from her home at $9.00\; am$, walks with a speed of $5\; km\; h^{-1}$ on a straight road up to her office $2.5\; km$ away, stays at the office up to $5.00\; pm$, and returns home by an auto with a speed of $25\; km\; h^{-1}$. Choose suitable scales and plot the $x-t$ graph of her motion.

(N/A) $1$. Time taken to reach the office:
Speed of the woman $= 5\; km\; h^{-1}$.
Distance between her office and home $= 2.5\; km$.
Time taken $= \frac{\text{Distance}}{\text{Speed}} = \frac{2.5}{5} = 0.5\; h = 30\; min$.
So, she reaches the office at $9.30\; am$.
$2$. Time spent at the office:
She stays at the office from $9.30\; am$ to $5.00\; pm$.
$3$. Time taken to return home:
Speed of the auto $= 25\; km\; h^{-1}$.
Distance $= 2.5\; km$.
Time taken $= \frac{\text{Distance}}{\text{Speed}} = \frac{2.5}{25} = 0.1\; h = 6\; min$.
She reaches home at $5.06\; pm$.
The $x-t$ graph shows the position $x$ (in $km$) on the $y$-axis and time $t$ on the $x$-axis. The graph is a straight line from $(9.00, 0)$ to $(9.30, 2.5)$, a horizontal line from $(9.30, 2.5)$ to $(5.00, 2.5)$, and a straight line from $(5.00, 2.5)$ to $(5.06, 0)$.