A car is moving along a straight road with a uniform acceleration . is passes through two points P and Q separated by a distance with velocity $30 k m / h$ and $40 k m / h$ respectively. the velocity of the car midway between P and Q is

33 \sqrt{5} k m / h

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20 \sqrt{2} k m / h

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25 \sqrt{2} k m / h

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35 k m / h

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Solution

The correct option is A $25 \sqrt{2} k m / h$
From the figure we can clearly see that;
$P L = L Q = s$ ; when $P Q = 2 s$ ;

Apply $v^{2} - u^{2} = 2 a s$ formula where $v = 40 k m / h r$ and $u = 30 k m / h r$ ;

$40^{2} - 30^{2} = 2 a (2 s)$

$1600 - 900 = 4 a s$
$a = \frac{175}{s} . . . . . . E q : 01$

Again apply formula where $v = ?$ and $u = i n i t i a l - v e l o c i t y = 30 k m / h r$ ;

$v^{2} - (30)^{2} = 2 a s$ ;
$v^{2} - 900 = 2 a (s)$ ;

$v^{2} - 900 = 2 (\frac{175}{s}) (s)$ ;

$v^{2} = 900 + 350$
$v^{2} = 1250$
$v = 25 \sqrt{2} k m / h r$

The required velocity of the card midway between P and Q is 25 $\sqrt{2}$ km/hr.

Option (C) is correct.

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A car is moving along a straight road with a uniform acceleration . is passes through two points P and Q separated by a distance with velocity 30km/h and 40km/h respectively. the velocity of the car midway between P and Q is

A car is moving along a straight road with a uniform acceleration . is passes through two points P and Q separated by a distance with velocity $30 k m / h$ and $40 k m / h$ respectively. the velocity of the car midway between P and Q is