If impulse I varies with time t as I text{ (k | vedclass

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(B) The impulse $I$ is defined as the change in momentum,$\Delta p = I$. Given $I = 20 t^2 - 40 t$.To find the time at which the change in momentum is

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$t=1$

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(B) The impulse $I$ is defined as the change in momentum,$\Delta p = I$. Given $I = 20 t^2 - 40 t$.To find the time at which the change in momentum is minimum,we differentiate $I$ with respect to $t$ and set it to zero:$\frac{dI}{dt} = \frac{d}{dt}(20 t^2 - 40 t) = 40 t - 40$.Setting $\frac{dI}{dt} = 0$ gives $40 t - 40 = 0$,which implies $t = 1 	ext{ s}$.To confirm this is a minimum,we check the second derivative: $\frac{d^2I}{dt^2} = 40$. Since $40 > 0$,the function has a minimum at $t = 1 	ext{ s}$.

If impulse $I$ varies with time $t$ as $I \text{ (kg m s}^{-1}) = 20 t^2 - 40 t$. The change in momentum is minimum at ........... $s$.

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