KCET · Physics · Motion In One Dimension
A body of mass \(m\) moving along a straight line covers half the distance with a speed of \(2 \mathrm{~ms}^{-1}\). The remaining half of the distance is covered in two equal time intervals with a speed of \(3 \mathrm{~ms}^{-1}\) and \(5 \mathrm{~ms}^{-1}\) respectively. The average speed of the particle for the entire journey is
- A \(\frac{3}{8} \mathrm{~ms}^{-1}\)
- B \(\frac{8}{3} \mathrm{~ms}^{-1}\)
- C \(\frac{4}{3} \mathrm{~ms}^{-1}\)
- D \(\frac{16}{3} \mathrm{~ms}^{-1}\)
Answer & Solution
Correct Answer
(B) \(\frac{8}{3} \mathrm{~ms}^{-1}\)
Step-by-step Solution
Detailed explanation
Let the total distance travelled by the body is \(2 S\). If \(\mathrm{t}_{1}\) is the time taken by the body to travel first half of the distance, then
\(\mathrm{t}_{1}=\frac{\mathrm{S}}{2}\)
Let \(\mathrm{t}_{2}\) be the time taken by the body for each time interval for the remaining half journey.
\(\therefore \quad \mathrm{S}=3 \mathrm{t}_{2}+5 \mathrm{t}_{2}=8 \mathrm{t}_{2}\)
So, average speed \(=\frac{\text { Total distance travelled }}{\text { Total time taken }}\)
\(=\frac{2 S}{t_{1}+2 t_{2}}\)
\(=\frac{2 S}{\frac{S}{2}+\frac{S}{4}}\)
\(=\frac{8}{3} \mathrm{~ms}^{-1}\)
\(\mathrm{t}_{1}=\frac{\mathrm{S}}{2}\)
Let \(\mathrm{t}_{2}\) be the time taken by the body for each time interval for the remaining half journey.
\(\therefore \quad \mathrm{S}=3 \mathrm{t}_{2}+5 \mathrm{t}_{2}=8 \mathrm{t}_{2}\)
So, average speed \(=\frac{\text { Total distance travelled }}{\text { Total time taken }}\)
\(=\frac{2 S}{t_{1}+2 t_{2}}\)
\(=\frac{2 S}{\frac{S}{2}+\frac{S}{4}}\)
\(=\frac{8}{3} \mathrm{~ms}^{-1}\)
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