Question

A body of mass $m$ moving along a straight line covers half the distance with a speed of $2m{s}^{-1}.$ The remaining half of the distance is covered in two equal time intervals with a speed of $3m{s}^{-1}$ and $5m{s}^{-1}$ respectively.The average speed of the particle for the entire journey is

• A. $\frac{3}{8}m{s}^{-1}$
• B. $\frac{8}{3}m{s}^{-1}$
• C. $\frac{4}{3}m{s}^{-1}$
• D. $\frac{16}{3}m{s}^{-1}$

Answer 1

Answer: (B)

$\frac{8}{3}m{s}^{-1}$

Let the total distance travelled by the body is $2s$.If $t_1$ is the time taken by the body to travel first half of the distance ,then
$t_1=\frac{S}{2}$
Let $t_2$ be the time taken by the body for each time interval for the remaining hal journey.
$S=3t_2+5t_2=8t_2$
So, average speed =$\frac{totaldistancetravelled}{totaltimetaken}$
$=\frac{2S}{t_1+2t_2}$
$=\frac{2S}{\frac{S}{2}+\frac{S}{4}}$
$=\frac{8}{3}m{s}^{-1}$