#### Question

A woman starts from her home at 9.00 am, walks with a speed of 5 km h^{–1} 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 h^{–1}. Choose suitable scales and plot the *x*-*t** *graph of her motion.

#### Solution 1

Speed of the woman = 5 km/h

Distance between her office and home = 2.5 km

`"Time taken" = "Distance"/"Speed"`

=2.5/5 = 0.5 h = 30 min

It is given that she covers the same distance in the evening by an auto.

Now, speed of the auto = 25 km/h

`"Time taken" = "Distance"/"Speed"`

=2.5/25 = 1/10 = 0.1 h = 6 min

The suitable *x*-*t* graph of the motion of the woman is shown in the given figure.

#### Solution 2

Distance covered while walking = 2.5 km.

Speed while walking = 5 km/h

Time taken to reach office while walking = (2.5/5 ) h=1/2 h

If O is regarded as the origin for both time and distance, then at t = 9.00 am, x = 0

and at t = 9.30 am, x = 2.5 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 AB in the graph.

Now, time taken to return home by an auto = 2.5/5 h =1/10 h =6 minute

So, at t = 5.06 pm, x = 0

This motion is represented by the straight line BC 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 km.