11. Distance-time graph

 

This graph shows the non-linear variation of the distance travelled by a vehicle with time (\(t\)). The shape of a graph plotted for an object travelling at a non-uniform speed is different from that of the object with uniform speed.

Example 1:

The time of arrivals and departures of a train at three stations \(A\), \(B\) and \(C\) and the distance of stations \(B\) and \(C\) from station \(A\) are given in the below table.

 

 

Plot and interpret the distance-time graph for the train, assuming that its motion between any two stations is uniform.

 

Solution:

 

 

We should take two axes on the graph paper. The \(X\)-axis represents time, while the \(Y\)-axis represents distance.

At 8:15 distance \(=\) \(0\ km\)
At 11:15 distance \(=\) \(120\ km\)
At 13:15 distance \(=\) \(180\ km\)

 

Example 2:

Feroz and his sister Sania go to school on their bicycles. Both of them start at the same time from their home but take different times to reach the school although they follow the same route.

 

The table below shows the distance travelled by them at different times.