Question

Two cars start off to race with velocities 4m/s and 2m/s and travel in a straight line with uniform acceleration 1m/s respectively.If they reach the final pointat the same instant,then the length of the path is​

Answer 1

Question:-

Two cars start off to race with initial velocities $\sf{4\ m\ s^{-1}}$ and $\sf{2\ m\ s^{-1}}$ respectively and travel in a straight line with uniform acceleration $\sf{1\ m\ s^{-2}}$ and $\sf{2\ m\ s^{-2}}$ respectively. If they reach the final point at the same instant, then find the length of the path.

Answer:-

$\huge\boxed{\quad\sf{24\ metres}\quad}$

Solution:-

• Velocity of first car = $\sf{4\ m\ s^{-1}}$

• Velocity of second car = $\sf{2\ m\ s^{-1}}$

• Acceleration of first car = $\sf{1\ m\ s^{-2}}$

• Acceleration of second car = $\sf{2\ m\ s^{-2}}$

According to first car, the length of the path is,

$\longrightarrow\sf{s=4t+\dfrac{1}{2}\cdot1\cdot t^2}$

$\longrightarrow\sf{s=4t+\dfrac{1}{2}t^2}$

And according to second car,

$\longrightarrow\sf{s=2t+\dfrac{1}{2}\cdot2\cdot t^2}$

$\longrightarrow\sf{s=2t+t^2\quad\quad\dots(1)}$

So,

$\longrightarrow\sf{4t+\dfrac{1}{2}t^2=2t+t^2}$

$\longrightarrow\sf{\dfrac{1}{2}t^2-2t=0}$

$\longrightarrow\sf{t^2-4t=0}$

$\longrightarrow\sf{t(t-4)=0}$

Since $\sf{t\neq 0,}$

$\longrightarrow\sf{t=4}$

Then the length of the path is,

$\longrightarrow\sf{s=2\times4+4^2}$

$\longrightarrow\sf{\underline{\underline{s=24\ m}}}$