Q.

For motion of an object along the x-axis, the velocity v depends on the displacement x as v = 3x2 - 2x, then what is the acceleration at x = 2 m.

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a

48 ms-2

b

80 ms-2

c

18 ms-2

d

10 ms-2

answer is B.

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Detailed Solution

Given v=3x2-2x; differentiating v, we get  dvdt=(6x-2)dxdt=(6x-2)v ⇒  a=(6x-2)3x2-2x Now put x=2m ⇒  a=(6×2-2)3(2)2-2×2=80 ms-2
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For motion of an object along the x-axis, the velocity v depends on the displacement x as v = 3x2 - 2x, then what is the acceleration at x = 2 m.