A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance.
A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance. The average velocity v is given by
(a) v = (v1 + v2)/2
(b) v = √(v1v2)
(c) 2/v = 1/v1 + 1/v2
(d) 1/v = 1/v1 + 1/v2.
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(c) 2/v = 1/v1 + 1/v2.
Explanation:
Time taken during first phase = x/v1 and during second phase = x/v2.
Total distance =2x
Total time taken = (x/v1)+(x/v2) = x(1/v1 +1/v2)
Average velocity =Total distance/Total time taken
v = 2x / x(1/v1 +1/v2)
=>v = 2/(1/v1 +1/v2)
=> 2/v = (1/v1 +1/v2) {Multiplying both sides by (1/v1 +1/v2)/v }
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