Question

A Man travel half length of a straight road with a constant speed of 20 metre per second and the travel the second half length of the road with a constant speed of 60 metre per second then calculate its average speed

Answer 1

let the whole distance =2x
to finish 1st half distance t1=x/20
to finish 2nd half distance t2=x/60
total time taken is T=x/15
av. velocity =2x/T=30 m/s

Answer 2

Answer:

30 m/sec

Explanation:\

Let's consider that the total length of the road is x. Then according to question, it is given that

Man travels half distance with a speed, $V_1\ =\ 20\ m/s$

hence time taken to travel first half distance, $t_1\ =\ \dfrac{distance}{speed}$

                                                                                  $=\ \dfrac{x}{2\times  v_1}$

                                                                                  $=\ \dfrac{x}{2\times 20}$

                                                                                 $=\ \dfrac{x}{40}\ sec$

Man travels another half distance with a speed, $V_2\ =\ 60\ m/s$

hence time taken to travel other half distance, $t_2\ =\ \dfrac{distance}{speed}$

                                                                                  $=\ \dfrac{x}{2\times  v_2}$

                                                                                  $=\ \dfrac{x}{2\times 60}$

                                                                                  $=\ \dfrac{x}{120}\ sec$

total time taken by man to cover the whole distance,$t\ =\ t_1+t_2$

                                                                                        $=\ \dfrac{x}{40}+\dfrac{x}{120}$

                                                                                        $=\ \dfrac{x}{30}$

So, the average speed can be given by

$V=\ \dfrac{\textrm{total distace travelled}}{\textrm{total time taken}}$

  $=\ \dfrac{x}{\dfrac{x}{30}}$

  = 30 m/sec

hence the average speed of the man is 30 m/sec.