Question

It is 260 km from Patna to Ranchi by air and 320 km by road. An aeroplane takes 30 minutes to go from Patna to Ranchi whereas a delux bus takes 8 hours. (a) Find the average speed of the plane. (b) Find the average speed of the bus. (c) Find the average velocity of the plane. (d) Find the average velocity of the bus.

Answer 1

(a) Average speed of the plane, s_avg $=\left(\frac{\mathrm{Total}\mathrm{distance}\mathrm{travelled}}{\mathrm{Total}\mathrm{time}\mathrm{taken}}\right)$$=\frac{260}{0.5}=520\mathrm{km}/\mathrm{h}$

(b) Average speed of the bus, _Savg$=\frac{320}{8}=40\mathrm{km}/\mathrm{h}$

(c) The plane moves in a straight path.
Average velocity = Average speed = $520\mathrm{km}/\mathrm{h}$ (Patna to Ranchi)

(d) Straight path distance from Patna to Ranchi = Displacement of the bus = 260 km
$\therefore {\overrightarrow{V}}_{avg}=\frac{260}{8}=32.5\mathrm{km}/\mathrm{h}$ (Patna to Ranchi)