1.14 Velocity  (Page 3/6)

Characteristics of motion : One dimensional, variable speed

(i) Total distance in the round trip = 120 + 120 = 240 Km

(ii) Displacement = 120 – 120 = 0

(iii) Average speed for the round trip

$$\begin{array}{lll}{v}_{\mathrm{OD}}=\frac{240}{9}=\mathrm{26.67\; km/hr}& \mathrm{and\; average\; velocity\; for\; the\; round\; trip\; :}& v_{\mathrm{OD}}=\frac{0}{9}=0\end{array}$$

(iv) Average speed during motion from O to C

$$\begin{array}{lll}{v}_{\mathrm{OC}}=\frac{120}{5}=\mathrm{24\; km/hr}& \mathrm{and\; average\; velocity\; :}& v_{\mathrm{OC}}=\frac{120}{5}=\mathrm{24\; km/hr}\end{array}$$

As magnitude of average velocity is positive, the direction of velocity is in the positive x – direction. It is important to note for motion in one dimension and in one direction (unidirectional), distance is equal to the magnitude of displacement and average speed is equal to the magnitude of average velocity. Such is the case for this portion of motion.

(v) The part of motion for which average velocity is equal in each direction.

By inspection of the plots, we see that time interval is same for motion from B to C and from C to B (on return). Also, the displacements in these two segments of motion are equal. Hence magnitudes of velocities in two segments are equal.

(vi) Compare speeds in the portion OB and BD.

By inspection of the plots, we see that the motor car travels equal distances of 60 m. We see that distances in each direction is covered in equal times i.e. 2 hrs. But, the car actually stops for 1 hour in the forward journey and as such average speed is smaller in this case.

$$\begin{array}{lll}{v}_{\mathrm{a,OB}}=\frac{60}{3}=\mathrm{20\; km/hr}& \mathrm{and}& v_{\mathrm{a,BD}}=\frac{60}{2}=\mathrm{30\; km/hr}\end{array}$$