A car is moving along a straight road with a uniform acceleration. It passes through two points $P$

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 $2 \mathrm{~km} / \mathrm{h}$ and $14 \mathrm{~km} / \mathrm{h}$ respectively. The velocity of the car midway between $P$ and $Q$ is\

Professor PC Thomas Classes · Answer

Let $P Q=s$ and $L$ is the midpoint of $P Q$ and $v$ be velocity of the car at point $L$.\ we know that $2 a s=v_Q^2-v_P^2$, which means $a s=\frac{v_Q^2-v_P^2}{2}$. is into the equation\ $\begin{gathered}v_M^2=v_P^2+2 a\left(\frac{s}{2}ight) \ v_M^2=v_P^2+a s\end{gathered}$
$$
\begin{gathered}
v_M^2=v_P^2+\frac{v_Q^2-v_P^2}{2} \
v_M^2=\frac{2 v_P^2+v_Q^2-v_P^2}{2} \
v_M^2=\frac{v_P^2+v_Q^2}{2} \
v_M=\sqrt{\frac{v_P^2+v_Q^2}{2}}
\end{gathered}
$$