travelling at a uniform speed of km/hr. Draw the time-distance graph and hence find (i) the constant of variation (ii) how far will it travel in minutes? (iii) the time required to cover a distance of km from the graph. Solution Let x be the time taken in minutes and y be the distance travelled in km.
Time taken x (in minutes) Distance y (in km) (i) Observe that as time increases, the distance travelled also increases. Therefore, the variation is a direct variation. It is of the form kx . Constant of variation k y = .
x Fig. . Scale x axis cm = unit y axis cm = unit y = ( . ) x Scale x axis cm = unit y axis cm = unit xy = ( , ) ( , ) ( , ) Fig.
. ( , ) Hence, the relation may be given as Þ = kx (ii) From the graph, = , if = then ´ km The distance travelled for minutes is km. (iii) From the graph, = , if = then ´ minutes (or) hours. The time taken to cover km is minutes (or) hours.
(ii) Indirect variation: The distance between Chennai and Madurai is (nearly) km. Think of a train that starts from Chennai and travels towards Madurai. As it increases speed more and more, the time taken for travel will decrease . In the following table speed v is given in km and time t is given in hours: Speed (v) (km/hr) Time (t) (hours) From the table it is clear that if you travel at a slower speed, the time increases and if the train is faster, the time decreases.