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

Answer: Distance covered while walking $=2.5 \mathrm{~km}$.
Speed while walking $=5 \mathrm{~km} / \mathrm{h}$
Time taken to reach office while walking $=(2.5 / 5) \mathrm{h}=1 / 2 \mathrm{~h}$
If $O$ is regarded as the origin for both time and distance, then at $t=9.00$ am, $x=0$
and at $\mathrm{t}=9.30 \mathrm{am}, \mathrm{x}=2.5 \mathrm{~km}$
OA is the x-t graph of the motion when the woman walks from her home to office. Her stay
in the office from $9.30$ am to $5.00$ pm is represented, by the straight line $A B$ in the graph.
Now, time taken to return home by an auto $=2.5 / 5 \mathrm{~h}=1 / 10 \mathrm{~h}=6$ minute
So, at $t=5.06 \mathrm{pm}, \mathrm{x}=0$
This motion is represented by the straight line $B C$ in the graph. While drawing the $x$-t graph,
the scales chosen are as under:
Along time-axis, one division equals 1 hour.
Along positive-axis, one division equals $0.5 \mathrm{~km}$.

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