A car moving along a straight highway with speed of `126 km h^(-1)` is brought to a stop within a distance of 200 m. What is the retardation of the car (assumed uniform), and how long does it take for the car to stop ?

Explanation

Initial velocity of car `v _(0) = 126 km//hr`
`= (126 xx 10 ^(3))/(3600)m//s = 35 ms^(-1)`
Finaly velocity of car v =0
Distance covered by car before it stops
`d = 200 m`
Constant acceleration a = ?
Time taken to stop t = ?
Now, from` v ^(2) - v _(0) ^(2) = 2 ad,`
`a = (v ^(2) - v _(0) ^(2))/(2d)`
`a = (0-(35) ^(2))/(2 xx 200) = (-35 xx 35)/(400)`
`a =- 3.06 ms ^(-2) " "therefore` Retaradation `= 3.06 ms ^(-2)`
Now, from `v =v _(0) + at,`
`0=35 + (-3.06) t `
` therefore 3.06 t = 35`
`t = (35)/(3.06)`
`therefore t= 11.44 s`