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A car accelerates from rest at constant ...

A car accelerates from rest at constant rate of `2ms^(-2)` for some time. Immediately after this, it retards at a constant rate of `4ms^(-2)` and comes to rest. The total time for which it remains in motion is 3 s. Taking the moment of start of motion as t = 0, answer the following questions.
What is the maximum speed attained by the car ?

Text Solution

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The area of v-t graph gives the displacement. Since the car moves in one direction, its total distance covered will be numerically equal to its displacement
S = 100 m (given)
`s=(1)/(2)(OB)(AB)+(1)/(2)(BC)(AB)``=(1)/(2)(t_(1)+t_(2))v_(0)`  where`v_(0)=maximum`
speed of the car
`(t_(1)+t_(2))`= T = 20 sec and s = 100 m
`rArr`  100 =`(1)/(2)(20)v_(0)rArrv_(0)=10m//sec`
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