### Chapter - 1 Motion

Q
##### Motion

Question:

Abdul, while driving to school, computes the average speed for his trip to be 20 kmh–1. On his return trip along the same route, there is less traffic and the average speed is 30 kmh–1. What is the average speed for Abdul’s trip?

Case I: While driving to school

Average speed of Abdul's trip = 20 km/h

Average speed = $= \frac{Total\ distance\ covered}{Total\ time\ taken}$

Total distance = Distance travelled to reach school = d

Let the total time taken = t1

$\therefore 20 = \frac{d}{t_1}$

${t_1} = \frac{d}{20} ---(i)$

Case II: While returning from school

Total distance = Distance travelled while returning from school = d

Now, total time taken = t2

$\therefore 30 = \frac{d}{t_2}$

${t_2} = \frac{d}{30} ---(ii)$

Average speed for Abdul's trip = $\frac{Total\ distance\ covered\ in\ the\ trip}{Total\ time\ taken}$

Where,

Total distance covered in the trip = d + d = 2d

Total time taken, t = Time taken to go to school + Time taken to return to school = ${t_1} + {t_2}$

Average speed $=\frac{2d}{(t_1+t_2 )}$

From equations (i) and (ii),

Average speed $= \frac{2d}{\frac{d}{20} + \frac{d}{30}} = \frac{2d}{\frac{3d+2d}{60}} = \frac {2d \times 60}{5d}$

Average speed $= \frac{120}{5} = 24\ m/s$

Hence, the average speed for Abdul's trip is 24 m/s.

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