Question

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. $33.3km/h$
• B. $20\sqrt{2}km/h$
• C. $25\sqrt{2}km/h$
• D. $35.5km/h$

Answer 1

Answer: (C)

Let $PQ=s$ and $L$ is the midpoint of $PQ$ and $v$ be velocity of the car at point $L$.
Using third equation of motion, we get
$(40{)}^2-(30{)}^2=2as$
or $a=\frac{(40{)}^2-(30{)}^2}{2s}=\frac{350}{s}$....(i)
Also, $v^2-(30{)}^2=2a\frac{s}{2}$
or $v^2-(30{)}^2=2\times \frac{350}{s}\times \frac{s}{2}$[Using (i)]
or $v=25\sqrt{2}km/hr$