Question

Akhil travels first half of the distance at 50 m/s and second half at 75 m/s. the total distance travelled is 3 km. find his average speed of travel for the entire journey.

Answer 1

time for the first case :
1500/50= 30 seconds
for the second case:
1500/75 =20 s
av. speed = 3000/(30+20) = 3000/50 = 60 m/s

Answer 2

The answer to the question is 60 m/s i.e the average speed of Akhil is 60 m/s .

CALCULATION:

As per the question, Akhil travels half of the distance at a speed 50 m/s.

Hence,the initial velocity of Akhil is given as $v_{1}=\ 50\ m/s$

Akhil travels second half of the distance at a speed of 75 m/s.

The total distance is calculated as 3 km.

The final velocity of Akhil is given as $v_{2}=\ 75\ m/s$

We are asked to calculate the average speed.

As the distance travelled in different instants are same, so the average speed is calculated as -

                                $v_{avg} =\ 2\frac{v_{1} v_{2}} {v_{1}+v_{2}}$

                                       $=\ 2\frac{50\times 75}{50+75}\ m/s$

                                       $=2\times \frac{50\times 75}{125}\ m/s$

                                       $=\ 60\ m/s$         [ans]