Question
A car, starting from rest, accelerates at a constant rate of 5 ms^{–2} for some time. It then retards at a constant rate of 10 ms^{–2} and finally comes to rest. If the total taken is 6 s, What is the maximum speed attained by the car?

5 ms^{–1}

10 ms^{–1}

20 ms^{–1}

40 ms^{–1}
medium
Solution
20 ms^{–1}
Let t_{1} be the time during which the car has an acceleration a_{1} = 5 ms^{–2}and t_{2} be the time during which the car has a deceleration a_{2} = –10 ms^{–2}. Since the car starts from rest, the maximum speed attained by the car . For time interval, this v is the initial speed and the final speed is zero. Therefore,
.
Thus,
= 2
.
Now,
.
Therefore
t_{1} = 4 s and t_{1} = 2 s.
Also
= 20 ms^{–1}.
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