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A Car Starts from Rest on a Half Kilometre 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. - Physics

Sum

A car starts from rest on a half kilometre 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.

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Solution

Let a be the maximum acceleration of the car for crossing the bridge.

From the above diagram,
ma = μR
(For more accelerations the tyres will slip)
ma = μmg
a = μg = 1 × 10 = 10 m/s2
To cross the bridge in minimum possible time, the car must be at its maximum acceleration.
u = 0, s = 500 m, a = 10 m/s2
From the equation of motion,
`s=ut+1/2at^2`
Substituting respective values
`500=0+(1/2)10t^2`

`=>t=sqrt100=10`s

Therefore, if the car's acceleration is less than 10 m/s2, it will take more than 10 s to cross the bridge. So, one cannot drive through the bridge in less than 10 s.

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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 6 Friction
Exercise | Q 17 | Page 98
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