Question

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

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

Answer 1

The Correct Option is A

Let the total distance travelled by the body is \(2 S\). 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 half journey.
\(\therefore \,\,\,\,S=3 t_{2}+5 t_{2}=8 t_{2}\)
So, average speed \(=\frac{\text { Total distance travelled }}{\text { Total time taken }}\)
\(=\frac{2 S}{t_{1}+2 t_{2}}\)
\(=\frac{2 S}{\frac{S}{2}+\frac{S}{4}}\)
\(=\frac{8}{3} \,ms ^{-1}\)

So, the correct answer is (A): \(\frac{8}{3}\,ms^{-1}\)