A car moving with a velocity 6.25 ,ms^{-1} is | vedclass

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(A) Given: Initial velocity $u = 6.25 \,ms^{-1}$, acceleration $a = -2.5 \sqrt{v} \,ms^{-2}$, and final velocity $v = 0$ (at rest).We know that accele

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$2$

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(A) Given: Initial velocity $u = 6.25 \,ms^{-1}$, acceleration $a = -2.5 \sqrt{v} \,ms^{-2}$, and final velocity $v = 0$ (at rest).We know that acceleration $a = \frac{dv}{dt}$.Substituting the given values:$\frac{dv}{dt} = -2.5 \sqrt{v}$Rearranging the terms to integrate:$\frac{dv}{\sqrt{v}} = -2.5 dt$Integrating both sides from initial velocity $u$ to final velocity $0$ over time $t$ from $0$ to $T$:$\int_{6.25}^{0} v^{-1/2} dv = \int_{0}^{T} -2.5 dt$$[2 \sqrt{v}]_{6.25}^{0} = -2.5 [t]_{0}^{T}$$2(\sqrt{0} - \sqrt{6.25}) = -2.5(T - 0)$$2(0 - 2.5) = -2.5T$$-5 = -2.5T$$T = \frac{5}{2.5} = 2 \,s$Therefore, the time taken for the car to come to rest is $2 \,s$.

$A$ car moving with a velocity $6.25 \,ms^{-1}$ is decelerated with $2.5 \sqrt{v} \,ms^{-2}$ (where $v$ is the instantaneous velocity). The time taken by the car to come to rest is: (in $\,s$)

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