Question

Stopping distance of vehicles:
When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity (v₀) and the braking capacity, or deceleration, –a that is caused by the braking. Derive an expression for stopping distance of a vehicle in terms of v₀ and a.

Answer 1

Dear Student

$$\begin{gathered} whenacartooksthebreak \\ thereisfrictionalforceF=-\mu mg \\ where\mu isthecofficeinentfriction \\ misthemass \\ gisthegravity \\ Whenthecartookthebreakittraveldis\mathrm{ta}ced \\ thenworkdoneW=F\times d \\ W=-\mu mg\times d \\ Thisworkdoneisdonebythekineticenergyofcarthen \\ W=-\frac{1}{2}m{v}^2 \\ takingnegativesignduetothefrictionwhichisinoppsitedirectionofmotion \\ Hence \\ W=-\mu mg\times d=-\frac{1}{2}m{v}^2 \\ d=\frac{v^2}{2\mu g} \\ thisisthestoppindis\tan ce \end{gathered}$$

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