Question

# A woman starts from her home at $9:00\mathrm{am}$ walks with a speed of $5{\mathrm{kmh}}^{-1}$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 $25{\mathrm{kmh}}^{-1}$. Choose suitable scales and plot the $\mathrm{x}-\mathrm{t}$ graph of her motion.

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Solution

## Step 1. Time at which women reached to office and homeDistance between the office and the home $\mathbf{=}2.5\mathrm{km}$The speed of the women $=5{\mathrm{kmh}}^{-1}$Time taken by the women to reach the office is, $\begin{array}{rcl}\mathrm{Time}\mathrm{taken}\mathrm{to}\mathrm{reach}\mathrm{office}& =& \frac{2.5}{5}\\ & =& 0.5\mathrm{h}\\ & =& 30\mathrm{min}\end{array}$At $9:30\mathrm{am}$ the women is at the office till $5\mathrm{pm}$.The speed of auto $=25{\mathrm{kmh}}^{-1}$The time taken by the women to reach back home is$\begin{array}{rcl}\mathrm{Time}\mathrm{taken}\mathrm{to}\mathrm{reach}\mathrm{home}\mathrm{back}& =& \frac{2.5}{25}\\ & =& 0.1\mathrm{h}\\ & =& 6\mathrm{min}\end{array}$At $5:06\mathrm{pm}$ women reach home.Step 2. Plot the graphNow plot the $x-t$ graph of her motion, where the women start from home at $9:00\mathrm{am}$ and reaches by $9:00\mathrm{am}$, and then she returns from the office at 5.00 pm and reaches home by 5.06 pm.The position-time graph will beThe time taken by the woman to reach back home is 30min At 9:30 am the women is at the office till 5 pm.The time taken by the women to reach back home is 6min at 5:06 pm women reach home.

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