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Question
A car moving along a straight highway with a 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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Solution
Initial velocity of the car, u = 126 km/h =`(126xx1000)/(60xx60)` ms-1 35 m/s
Final velocity of the car, v = 0
Distance covered by the car before coming to rest, s = 200 m
Retardation produced in the car = a
From third equation of motion, a can be calculated as:
`v^2 - u^2 = 2as`
∴ `(0)^2 - (35)^2 = 2 xx a xx 200`
`a = (35 xx 35)/(2xx200) = -3.06 "m/s"^2`
From first equation of motion, time (t) taken by the car to stop can be obtained as:
v = u + at
`t = (v-u)/a = (-35)/-3.06 = 11.44 s`
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