Question

# A car covers the first half of the distance between two places at $$40kmph$$ and the other half at $$60kmph$$. The average speed of the car is :

A
40kmph
B
48kmph
C
50kmph
D
60kmph

Solution

## The correct option is B $$48kmph$$Given,$$v_1=40kmph$$$$v_2=60kmph$$Lets consider $$d=$$ total distance The time taken to compete half distance with speed $$v_1$$,$$t_1=\dfrac{d}{2v_1}$$The time take to complete second half distance with speed $$v_2$$$$t_2=\dfrac{d}{2v_2}$$Total time, $$t=t_1+t_2$$$$t=\dfrac{d}{2v_1}+\dfrac{d}{2v_2}$$$$t=\dfrac{d}{2}(\dfrac{1}{v_1}+\dfrac{1}{v_2})=\dfrac{d(v_1+v_2)}{2v_1v_2}$$. . . . . . . . .(1)The average speed of the car is given,$$v_{avg}=\dfrac{d}{t}$$$$v_{avg}=\dfrac{2v_1v_2}{v_1+v_2}$$   (from equation 1)$$v_{avg}=\dfrac{2\times 40\times 60}{40+60}=48kmph$$The correct option is B.Physics

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