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  4. A car moving with a speed of 40 km/h be stopped by applying brakes after at least 2 m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping distance:

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Q. A car moving with a speed of 40 km/h be stopped by applying brakes after at least 2 m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping distance:

JIPMERJIPMER 2001Motion in a Plane

Solution:

$ {{\upsilon }^{2}}={{u}^{2}}-2as $ (from equation of motion) $ s=\frac{{{u}^{2}}}{2a}=\frac{m{{u}^{2}}}{2am}=\frac{m{{u}^{2}}}{2F} $ $ s\propto {{u}^{2}} $ Hence $ \frac{{{s}_{1}}}{{{s}_{2}}}={{\left( \frac{{{u}_{1}}}{{{u}_{2}}} \right)}^{2}} $ or $ \frac{2}{{{s}_{2}}}=\frac{1}{4} $ $ {{s}_{2}}=8\,m $