Question

A particle moving in a straight line covers half the distance with speed of $3 ms^{-1}$. The other half of the distance is covered in two equal time intervals with speed of $4.5\, ms^{-1}$ and $7.5\, ms^{-1}$ respectively. The average speed of the particle during this motion is

• A. 5.0
• B. 5.5
• C. 5.8
• D. 4.0
• E. 4.8

Answer 1

Answer: (D)

$
\begin{aligned}
t _{1} &=\frac{\frac{ S }{2}}{3}=\frac{ S }{6} \\
\frac{ S }{2} &=4.5 \times t _{2}+7.5 t _{3} \Rightarrow 12 t _{2}=\frac{ S }{2}
\end{aligned}
$
We have $t _{2}= t _{3}$
Total time $t = t _{1}+ t _{2}+ t _{3}=\frac{ S }{6}+\frac{ S }{24}+\frac{ S }{24}=\frac{ S }{4}$
Average of $\frac{S}{t}=\frac{S}{\frac{S}{4}}=4 m / s$