A car starts from rest on a half kilometer long bridge. The coefficient of friction between the tyre and the road is 1.0. Show that one cannot drive through the bridge in less than 10 s.
From the above diagram,
ma = μR
ma = μmg
a = μg = 1 × 10 = 10 m/s2
If the driver wants to cross the bridge in minimum time, he/ she must be at its maximum acceleration.
initial velocity u = 0,
Distance s = 500 m,
acceleration a = 10 m/s2
From the equation of motion,
s=ut + 
at2
Substituting respective values
500=0+
(10)(10) 2
⇒t=100=10 s
Therefore, car will take more than 10 sec to cross the bridge if the acceleration is less than 10 m/s2.
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