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

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

(a) 33.3 km/h

(b) 20√2 km/h

(c) 25√2 km/h

(d) 35 km/h

Answer :  (c) 25√2 km/h

\( v^2 = u^2 + 2as \)

equation 1 :-  \(  v^2 = 30^2 + 2a\left(\frac{d}{2}\right) \)

equation 2 :-  \(  40^2 = v^2 + 2a\left(\frac{d}{2}\right) \)

\( \text{equation 1} - \text{equation 2} \Rightarrow v^2 - 40^2 = 30^2 - v^2  \)

\( \Rightarrow 2v^2 = 30^2 + 40^2 = 2500 \)

\( \Rightarrow v^2 = 1250 \)

\( \Rightarrow v = 25\sqrt{2} \)