A woman starts from her home at 9:00 am, walks with a speed of 5 km/h in a straight road up to her office 2.5 km away, stays at the office until 5:00 pm, and returns home by auto with a speed of 25 km/h. Choose suitable scales and plot the distance-time (x-t) graph of her motion.
Answer (2)
To plot the distance-time (x-t) graph for the woman's motion, let's look at her journey step-by-step as follows:
A Woman's Journey to Her Office:
She starts from home at 9:00 am.
Walks to her office, which is 2.5 km away.
Walking speed: 5 km/h.
To find the time taken to reach the office:
Time = Speed Distance = 5 km/h 2.5 km = 0.5 hours .
This means she reaches her office at 9:30 am.
Staying at the Office:
She stays in her office from 9:30 am to 5:00 pm, which is 7.5 hours.
During this period, her distance from home remains constant at 2.5 km.
Return Journey Home:
Leaves the office at 5:00 pm.
Returns home in an auto with a speed of 25 km/h.
To find the time taken to return home:
Time = 25 km/h 2.5 km = 0.1 hours (6 minutes) .
Thus, she reaches home by 5:06 pm.
Plotting the Distance-Time Graph:
Initial Point (Home): At 9:00 am, the distance is 0 km.
9:30 am: The distance is 2.5 km (Office).
Constant Distance: From 9:30 am to 5:00 pm, the distance remains 2.5 km.
Return Journey: Starts at 5:00 pm and ends at 5:06 pm, back to 0 km.
Choose a suitable scale:
Time could be represented on the x-axis, with each hour as a unit.
Distance could be represented on the y-axis, with each km as a unit.
With this scale, the plot would include:
A straight line rising from (9:00, 0) to (9:30, 2.5).
A horizontal line from (9:30, 2.5) to (17:00, 2.5).
A declined line from (17:00, 2.5) to (17:06, 0).
This graph visually displays her journey with time on the horizontal axis and distance on the vertical axis.
The distance-time graph of the woman's journey consists of three segments: she walks to her office at 5 km/h, stays there for 7.5 hours, and then returns home at 25 km/h. The graph will have a rising line to the office, a horizontal line during her stay, and a declining line back home. Suitable scales for time and distance should be chosen to plot this journey clearly.
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