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Applied Mechanics - Engineering

Q1:

The displacement of a particle which moves along a straight line is given by S = 4t3 + 3t2 - 10 where S is in meters and t is in seconds. The time taken by the particle to acquire a velocity of 18 m/sec from rest, is

A sec

B 1 sec

C 1.5 sec

D 1.5 sec.

ANS:B - 1 sec

let ds/dt = 12t sqa + 6t - 18 = 0(By Differentation)

Now, 2t Squa + t - 3 = 0.
Hence, 2tsqua - 2t + 3t - 3 = 0.
OR
2t(t - 1) + 3(t - 1) =0.

So (2t + 3) (t - 1) = 0 -> 2t + 3=0 And t - 1=0.
So t = 1 (Because 2t = -3 And t = -1.5 which is not possiable).