A car travels a distance $100 m$ with a constant acceleration and average velocity of $20 m s^{- 1}$ . The final velocity acquired by the car is $25 m s^{- 1}$ . Find the initial velocity.

15 m s^{- 1}

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10 m s^{- 1}

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30 m s^{- 1}

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0 m s^{- 1}

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Solution

The correct option is A $15 m s^{- 1}$
$S = 100 m, v_{a v g} = 20 m / s, v = 25 m / s$
Time taken to cover the distance, $t = \frac{S}{v_{a v g}} = \frac{100}{20} = 5 s$
From, $v = u + a t$
$25 = u + a * 5$
$a = \frac{25 - u}{5}$
Putting the value of $a$ in $v^{2} = u^{2} + 2 a S$
$25^{2} = u^{2} + 2 * \frac{25 - u}{5} * 100$
$u^{2} - 40 u + 375 = 0$
On solving, we get two values of u as $15 m / s a n d 25 m / s$ .
Since, final velocity is 25 m/s, initial velocity is 15 m/s.

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A car travels a distance 100m with a constant acceleration and average velocity of 20 ms−1. The final velocity acquired by the car is 25 ms−1. Find the initial velocity.

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