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

Answer 1

Answer: (C)

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