Question

A particle travels half of the distance of a straight journey with a speed $6m/s$. The remaining part of the distance is covered with speed $2m/s$ for half of the time and with speed $4m/s$ for other half of time. The average speed of the particle is :

• A. $3m/s$
• B. $4m/s$
• C. $\frac{3}{4}m/s$
• D. $5m/s$

Answer 1

The correct option is B $4m/s$

Let total distance covered in the entire journey is $2x$.

Let $t_1$ is the time to cover half of the distance with a speed of $6m/s$.

So,$t_1=\frac{x}{6}............\left(1\right)$

Let, for the second part total time is $t_2$.

Let the distance covered in first half time with a speed of $2m/s$ is $x_1$. So, $x_1=\frac{t_2}{2}\times 2=t_2............\left(2\right)$

For the second half the distance covered with a speed of $4m/s$is $x_2$. So, $x_2=\frac{t_2}{2}\times 4=2t_2..........\left(3\right)$

Now,

$x_1+x_2=x$

$t_2+2t_2=x$

$t_2=\frac{x}{3}............\left(3\right)$

Hence, $totaltime=t_1+t_2=\frac{x}{6}+\frac{x}{3}$

Now , $averagespeed=\frac{totaldistance}{totaltime}$

$s=\frac{2x}{\frac{x}{6}+\frac{x}{3}}=\frac{2x}{3x}\times 6$

$s=4m/s$