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{tex}\vec { a } \times \vec { b } = | \vec { a } | | \vec { b } | \sin \theta \hat { n }{/tex}
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In right triangle trigonometry (for acute angles only), the tangent is defined as the ratio of the opposite side to the adjacent side. The unit circle definition is tan(theta)=y/x or tan(theta)=sin(theta)/cos(theta).
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The binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial (<i>x</i> + <i>y</i>)<i>n</i> into a sum involving terms of the form <i>a x</i><i>b</i> <i>y</i><i>c</i>, where the exponents b and c are non negative integers with <i>b</i> + <i>c</i> = <i>n</i>, and the coefficient a of each term is a specific positive integer depending on n and b. For example (for <i>n</i> = 4),{tex}( x + y ) ^ { 4 } = x ^ { 4 } + 4 x ^ { 3 } y + 6 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 } + y ^ { 4 }{/tex}
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On differentiating, displacement, we get velocity.
Velocity(v) = {tex}\frac { d x } { d t } = 12 - 3 t ^ { 2 }{/tex}
Again on differentiating, velocity, we get acceleration.
Acceleration(a) = {tex}\frac { d v } { d t } = - 6 t{/tex}
When velocity becomes zero,
12 - 3t2 = 0 {tex}\implies t = 2{/tex}
Therefore,
= -6t = -6 x 2 = -12 ms-2
The acceleration is negative i.e, retardation.

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Nisham Singh 6 years, 6 months ago
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