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Question

A car moves towards north at a speed of 54 km/h for 1 h. Then it moves eastward with same speed for same duration. The average speed and average velocity of car for complete journey is :


A
54km/h,0
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B
15m/s,152m/s
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C
0,0
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D
0,542km/h
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Solution

The correct option is B $$15m/s,\dfrac{15}{\sqrt{2}}m/s$$
Average speed is the ratio of the total distance travelled by the car and the total time taken, 
$$Speed_{avg}=\dfrac{15t+15t}{t+t}$$ ($$\because 54km/s=15m/s$$)
or, $$Speed_{avg}=15m/s$$
Average velocity will be the ratio of displacement and time. 
The car moves north first and then east. The shortest distance will be the hypotenuse of the triangular path. 
$$v_{avg}=\dfrac{15\sqrt{2}t}{t+t}$$
or, $$v_{avg}=\dfrac{15\sqrt{2}}{2}$$
or, $$v_{avg}=\dfrac{15}{\sqrt{2}}$$ is our required answer. 
The correct answer is therefore option (B). 

Physics

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