Example of motion in one dimension | Learn Physics

Example of motion in one dimension

Question: Two towns A anb B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km/h, in the direction A to B notices that a bus goes past him every 18 minutes in the direction of his motion and every minute in the oppositive direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road.

Solution:

Let v km/h be the constant speed with which the buses ply between the towns A and B.

The relative speed of the bus, from A to B (i.e. in the direction of motion of cyclist) with respect to the cyclist = (v -20)km/h.

The relative speed of the bus, from B to A with respect to the cyclist =(v+20)km/h.

The distance travelled by the bus in the time T hour =vT

As per question : vT/(v-20)=18/60      or     60vT=18v-360    …………(i)

And    vT/(v+20)=   6/60            or 60vT = 6v + 120    ………………….(ii)

From (i) and (ii), we have

18v-360 = 6v+120

12v=480                     or                  v= 40km/h.

Putting the value in (i) we have,

60 × 40 × T = 18 × 40 – 360 = 360                 or       T = 360h/60×40 = 9 min.

 

Ans . 9 min is the period T of the bus service