Question

A student goes from his to his friend`s house with speed ` v_1`. Finding the door of his friend`s home closed, he returns back to his own house with the speed ` v_2`. Then the averge speed and net displacement of student is [consider distance between two houses be S].
A. (a) ` (v_1+v_2)/2 , 0`
B. (b) ` sqrt ( v_1 v_2 , 2 S`
C. (c ) (2 v_1 v_2 )/(v_1+v_2), 0`
D. (d) ` v_1 v_2, S`

Answer 1

Correct Answer - C
As (S) the distance between two houses. Time taken by a student in going in one direction,
` t_1 = S/v_1`
Time taken by student coming back, ` t_2 = S/v-2`
Total time , ` t_1 +t_2`
` =S/v-1 + S/v-2 = S [ 1 /v-1 + 1/v_2} ` or ` t= S [ (v_1 +v_2)/(v_1v_1)]`
Total distance travelled ` = S+ S=2 S`
:. Average speed ` = ( 2S(v_1v_2)/(S9v-1 +v_2)) = ( 2 v-1 v_2)/(v_1 +v_2)`
As he returnd back ot his initail position, so net displacrment is zero`.