A motorcyclist drives from point P to Q on a straight horizontal road with a uniform speed of 54 km/h and returns back with a speed of 36 km/h. If he completes the first half of the journey (i.e., from P to Q) in 50 s, then which of the following statements is/are correct?
(i) average velocity for the complete journey is zero.
(ii) shortest distance between P and Q is 750 m.
(iii) average speed for the complete journey is 15 m/s.
(iv) displacement for the complete journey is zero.
?

Dear Student,
Given,

• Motorcyclist drives from P to Q with uniform speed u = 54 km/h
• Motorcyclist drives back from Q to P with uniform speed v = 36 km/h
• Time taken to go from P to Q, t₁ = 50 s

(i)
Total displacement of the motorcyclist in the journey, d = 0
Average velocity, $v_{avg}=\frac{Total displacement}{total time}=\frac{0}{total time}=0$
Option (i) is CORRECT.
(ii)
Distance between P and Q, $x=u{t}_1=\frac{54km/h\times 1000m/km}{3600s/h}\times 50s=750 m$
Since, this is the straight line distance so the shortest distance between P and Q is 750m.
Option (ii) is CORRECT.

(iii)
Total distance travelled, $X=2x=2\times 750m=1500m$
Time taken in the journey from Q to P, $t_2=\frac{x}{v}=\frac{750m}{36km/h\times {\displaystyle \frac{1000m/km}{3600s/h}}}=75s$
Average speed for the complete journey,
$V_{avg}=\frac{Total dis\tan ce}{total time}=\frac{1500m}{50s+75s}=12m/s$
(iii) option is INCORRECT.

(iv)
Since, the motorcyclist returns back to the initial position P, the total displacement of the motorcyclist in the journey, d = 0.
Option (iv) is CORRECT.

Regards