Question

a car travells 1st half of distance with forty km per hour and 2nd half with 60 km per hour then calculate average speed of car​

Answer 1

Solution :-

Let us consider that the car travels from point A to B with a speed of 40 km / hr and from point B to C with a speed of 60 km / hr

Let the total distance traveled by the car be d

From A to B

• Speed (S 1 ) = 40 km / hr

• Let the time taken by the car  be t 1 and the distance covered be d /2

we know that ,

➨ S 1  = d 1 / t 1

On rearranging ,

➨ t 1  =d 1/ S1  

➨ t 1 = d / 2 x40

➨ t 1 = d / 80

From point B to C

• Speed (S 2 ) = 60 km / hr

• Let the time taken by the car  be t 2 and the distance covered be d /2

we know that ,

➨ S 2 = d 2 / t 1

On rearranging ,

➨ t 2  =d 2/ S2  

➨ t 2 = d / 2 x 60

➨ t 2 = d / 120

Average speed of the car is given by the formula ,

$\implies\mathtt{ Avg.speed =\dfrac{ total \:distance}{ total\: time}}$

$\implies\mathtt{ Avg.speed =\dfrac{ d}{ t_1 + t_2 }}$

$\implies\mathtt{ Avg.speed =\dfrac{ d}{ \dfrac{d}{80} + \dfrac{d}{120} }}$

$\implies\mathtt{ Avg.speed =\dfrac{ d}{d(\dfrac{1}{80} + \dfrac{1}{120} ) }}$

$\implies\mathtt{ Avg.speed =\dfrac{ 1}{\dfrac{3+2}{240} }}$

$\implies\mathtt{ Avg.speed =\dfrac{ 240}{5}}$

$\implies\mathtt{ Avg.speed =48\dfrac{m}{s }}$

The average speed of the car = 48 m /s