Question

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

Answer 1

Hint:
In this question, we need to plot the position-time graph of the women. Here, the starting time of a woman is given also the distance and travelling speeds are given for women between her home and the office, so by using speed, time, distance formula we find the time and then graph is plotted.

Complete step by step solution:
Speed of the women\[ = 5km{h^{ - 1}}\]
Distance of her office from home\[ = 2.5km\]
As we know the distance travelled by an object between the two points is given as the product of the speed of the object and the time taken by the object to travel that distance given as
\[d = s \times t - - (i)\]
So the time taken by the women to travel from home to office will be
\[
  t = \dfrac{d}{s} \\
   = \dfrac{{2.5}}{5} \\
   = \dfrac{1}{2} \\
   = 0.5h \\
   = 30\min \\
 \]
Hence the time taken by women to travel to office from her home\[ = 30\min \]
Now it is given that in evening while returning from office women takes auto to travel to home, where
The speed of the auto is\[ = 25km{h^{ - 1}}\]
Hence the time taken by women to travel same distance from home by auto to office will be
\[
  t = \dfrac{d}{s} \\
   = \dfrac{{2.5}}{{25}} \\
   = \dfrac{1}{{10}} \\
   = 0.1h \\
   = 6\min \\
 \]

Hence the time taken by women to travel to office from her home by auto\[ = 6\min \]

Now plot the x-t graph of her motion, where women start from home at 9.00 am and reach by 9.30 am and then she returns from office at 5.00 pm and reaches home by 5.06 pm.

Note:
Speed is the measure of how quickly an object can move from one place to another and it is equal to the ratio of distance travelled by object by the time taken by object, given \[s = \dfrac{d}{t}\]