Motion of a particle is given by the equation | vedclass

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(A) The position of the particle is given by $s(t) = 3t^3 + 7t^2 + 3t + 8$.Velocity $v(t)$ is the first derivative of position with respect to time: $

Vedclass · Accepted Answer

$32$

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(A) The position of the particle is given by $s(t) = 3t^3 + 7t^2 + 3t + 8$.Velocity $v(t)$ is the first derivative of position with respect to time: $v(t) = \frac{ds}{dt} = \frac{d}{dt}(3t^3 + 7t^2 + 3t + 8) = 9t^2 + 14t + 3$.Acceleration $a(t)$ is the derivative of velocity with respect to time: $a(t) = \frac{dv}{dt} = \frac{d}{dt}(9t^2 + 14t + 3) = 18t + 14$.At $t = 1 \ s$,the acceleration is $a(1) = 18(1) + 14 = 18 + 14 = 32 \ m/s^2$.

Motion of a particle is given by the equation $s = (3t^3 + 7t^2 + 3t + 8) \ m$. The acceleration of the particle at $t = 1 \ s$ is: (in $m/s^2$)

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