Questions in differentiation

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If the distance $s$ traveled by a particle in time $t$ is$s=a\sin t+b\cos 2t$ , then the acceleration at $t = 0$ is
A particle moves so that $S=6+48t-{{t}^{3}}$ . The direction of motion reverses after moving a distance of
If the volume of a spherical balloon is increasing at the rate of $900 cm^3$ per sec, then the rate of change of radius of balloon at instant when radius is 15cm [in cm/sec]
If the path of a moving point is the curve $x=at$ , $y=b\sin at$ , then its acceleration at any instant
If the rate of increase of area of a circle is not constant but the rate of increase of perimeter is constant, then the rate of increase of area varies
A stone thrown vertically upwards rises $s$ metre in $t$ seconds, where $s=80t-16{{t}^{2}}$ , then the velocity after 2 seconds is
A particle moves along a straight line so that its distance s in time t sec is $s=t+6{{t}^{2}}-{{t}^{3}}$ . After what time is the acceleration zero
The distance $s$ metre covered by a body in $t$ seconds is given by $s=3{{t}^{2}}-8t+5,$ the body will stop after
The rate of change of $\sqrt{({{x}^{2}}+16)}$ with respect to $\frac{x}{x-1}$ at $x=3$ is
The speed $v$ of a particle moving along a straight line is given by $a+b{{v}^{2}}={{x}^{2}}$ (where x is its distance from the origin). The acceleration of the particle is

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