Question

An automobile, travelling at 40km/h, can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 80 km/h, the minimum stopping distance, in metres, is

Answer 1

Given :

initial velocity ( u ) = 40 km/hr

                              = 40 × 1000 m / 3600 s

                              = 40 × 5 / 18 m/s

                              = 200 / 18 m/s .

Final velocity ( v ) = 0 m/s

Distance ( S ) = 40 m .

v² = u² + 2 a S

= > 0 = u² + 2 a S

= > ( 200 / 18 )² + 2 × 40 × a = 0

= > 80 a = - 40000 / 324

= > a = - 500 / 324

When initial velocity = 80 km/hr

                                  = 80 × 5/18 m/s

                                  = 400/18 m/s

v² = u² + 2 a S

= > u² + 2 a S = 0

= > ( 400 / 18 )² + 2 × - 500 / 324 × S = 0

= > 1,60,000 / 324 - 1000 / 324 S = 0

= > 1,6000 / 324 S = 40,000 / 324

= >  S = 1,60,000 / 1000

= > S = 160 m

ANSWER :

The distance would be 160 m