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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)3x2−2xNow put x = 2 m⇒ 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.