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Question

(D) The displacement is given by $s = 3t^3 + 7t^2 + 14t + 8$.To find the velocity $v$,we differentiate $s$ with respect to time $t$:$v = \frac{ds}{dt}

Vedclass · Accepted Answer

$32$

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(D) The displacement is given by $s = 3t^3 + 7t^2 + 14t + 8$.To find the velocity $v$,we differentiate $s$ with respect to time $t$:$v = \frac{ds}{dt} = \frac{d}{dt}(3t^3 + 7t^2 + 14t + 8) = 9t^2 + 14t + 14$.To find the acceleration $a$,we differentiate the velocity $v$ with respect to time $t$:$a = \frac{dv}{dt} = \frac{d}{dt}(9t^2 + 14t + 14) = 18t + 14$.At time $t = 1 \ s$,the acceleration is:$a = 18(1) + 14 = 18 + 14 = 32 \ m/s^2$.

The displacement equation for a particle is $s = 3t^3 + 7t^2 + 14t + 8 \ m$. Its acceleration at time $t = 1 \ s$ is ....... $m/s^2$.

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