Question

A river is

32 km

away from Nikita's house. There is a hillock on the way. Nikita left for the river one morning on her bicycle. She reached the hillock after 2 hours, pedalling at a speed of

5 kmph

. Since she could not cycle up the slope, she continued on foot, walking for an hour at a speed of

3 kmph

, and reached the top of the hillock. From there the road was all downhill. She rode her bicycle at a speed of

18 kmph

and reached the bottom of the hillock in half an hour. She then rested under a tree for half an hour. Refreshed after a rest, she cycled at a speed of

5 kmph

and reached the river in 2 hours. Draw a graph of Nikita's journey from her home to the river.

Accepted Answer

The graph of Nikita's journey from home to river is shown below.

The change in the position of an object with time can be represented on the distance-time graph adopting a convenient scale of choice. In this graph, time is taken along the x-axis and distance is taken along the y-axis.

The journey of Nikita can be broken down into $5$ parts as shown in the figure.

The curve AB represents her cycle journey to reach hillock at a speed of $5 {kmh}^{- 1}$ . Also, it is given that the time taken by Nikita to reach hillock is given as $2$ hours.
Therefore, the distance covered by Nikita = $5 \times 2 = 10 km$ . Thus, the curve AB starts from origin, and it is a straight line and ends at a point which is obtained by drawing perpendiculars from points corresponding to $2$ in x-axis and $10$ in y-axis. The curve is straight as the speed of Nikita is constant during this motion.

The curve BC represents the motion of Nikita by foot. It is given that the time of journey is one hour at a rate of $3 {kmh}^{- 1}$ . So, the distance travelled in this interval = $3 \times 1 = 3 km$ .
So the total distance covered by Nikita by this time = $10 + 3 = 13 km$ .
The curve starts at B and ends at a point obtained by drawing perpendiculars from points $3$ in x-axis and $13$ from the y-axis.

The curve CD represents the downhill motion of Nikita at a rate of $18 {kmh}^{- 1}$ . This fast movement lasted for half an hour and the distance covered during this period is $9 km$ .

The curve DE is parallel to the time axis. This implies that during this period there is no change in position with respect to time and hence, it represents the state of rest.

Finally, the curve EF represents her journey after the refresher break. She travelled for two hours at a rate of $5 {kmh}^{- 1}$ . The slope of the curve EF is similar to that of AB as the speed of travel was same in both instances.

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