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In the above example, the average accele...

In the above example, the average acceleration of the particle in the interval t = 1 to t = 3 sec will be-

A

12 a – 2b

B

2b – 12 a

C

2a – 12b

D

12b – 2a

Text Solution

Verified by Experts

In the light of above example, we have
` (dx)/(dt) = 2at - 3bt^(2)`
Now velocity at t = 1 sec, ` v_(1) = ((dx)/(dt))_(t=1) = 2a - 3b`
and that at ` t = 3 sec , v_(2) = ((dx)/(dt))_(t= 3) = 6a - 27 b `
Thus average acceleration ` a_(av) = (v_(2) - v_(1))/(t_(2) - t_(1))`
` = (6a - 27b - 2a + 3b)/(3-1) = (4a - 24b)/(2) = 2a - 12b `
Hence correct answer is (C)
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