A car moving with a speed of 40   k m h r can be stopped by applying brakes at least after 2 m. If the…

A car moving with a speed of 40  km hr can be stopped by applying brakes at least after 2 m. If the same car is moving with a speed of 80  km hr , what is the minimum stopping distance?
  1. 8 m
  2. 6 m
  3. 4 m
  4. 2 m

Solution

Using   v 2 − u 2  = 2as  we  get−

a =  v 2 − u 2 2s

= − u 1 2 2s  , where  u 1  = 40  km hr

For same retarding force   s ∝  u 2

∵   s 2 s 1  =  u 2 2 u 1 2

⇒  s 2 s 1  =  ( 80 40 ) 2  = 4

∴  s 2  = 4 s 1

= 8m

method II

If F is retarding force and s the stopping distance, then   1 2 m v 2  = Fs

For same retarding force,   s α  v 2

∴  s 2 s 1  =  ( v 2 v 1 ) 2  =  ( 80  km hr 40  km hr ) 2  = 4

∴  s 2  = 4 s 1  = 4×2 = 8m

Note: Here, for both the cases, acceleration (retardation) is the same.

Asked in: JEE Mains - Motion In One Dimension - Test 2

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