Question

for motion of an object along the x axis,the velocity v,depends on the displacement x as v=( 2x^2-x), then what is the acceleration at x=2m
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Answer 1

v = 2x²-x

We know,

Differentiation of velocity gives acceleration,

a= dv/dx {y = 2x²-x}

a= d2x²-x/dx

a= d(2x²)/dx + d(-x)/x

a = 2×2x²-¹ + -x¹-¹

a = 4x-1

Acceleration at x = 2m

a = 4×2-1 = 8-1 = 7

Acceleration at x = 2m is 7m/s²

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