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# A car moving along a straight highway with speed of 126 km h raise to minus 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

Q 3.6     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 ?

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Initial velocity(u)=126 km h-1=35 m s-1

Final velocity(v)=0

Distance travelled before coming to rest(s)=200m

Using the third equation of motion

$\\v^{2}-u^{2}=2as\\ a=\frac{v^{2}-u^{2}}{2s}\\ a=\frac{-35^{2}}{200}\\ a=-3.0625\ m\ s^{-2}$

Using the first equation of motion

$\\v=u+at\\ t=\frac{v-u}{a}\\ t=\frac{0-35}{-3.0625}\\ t=11.428\ s$

The retardation of the car is 3.0625 m s-2 and it takes 11.428 seconds for the car to stop.

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