Motion in a Straight Line

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Question : 3
Total: 27
A woman starts from her home at 9.00 am, walks with a speed of 5 km h1 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 h1. Choose suitable scales and plot the (x-t) graph of her motion.
Solution:  
From home to office : Time at which she leaves home for the office=9am.
speed =5 km h1; distance =2.5 km
Therefore, time taken to reach the office,
t=
distance
speed

=
2.5 km
5 km h1

=0.5 h=30 min
Thus, time at which she reaches her office = 9.30 am.
Between 9.30 am to 5 pm, she remains in her office i.e. at a distance of 2.5 km from her home.
From office to home : Time at which she leaves her office = 5 pm.
Speed =25 km h1, distance =2.5 km
Therefore, time taken to reach the home, t=
2.5 km
25 kmh1

=
1
10
h
=6 min

Therefore, time at which she reaches her home = 5.06 pm.
Hence, (x-t) graph of her motion will be as shown in figure.
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