Question

A particle moving in a straight line covers half the distance with speed of $3m{s}^{-1}$. The other half of the distance is covered in two equal time intervals with speed of $4.5m{s}^{-1}$ and $7.5m{s}^{-1}$ 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)

$<br/>\begin{array}{rl}<br/>t_1& =\frac{\frac{S}{2}}{3}=\frac{S}{6}\\ <br/>\frac{S}{2}& =4.5\times t_2+7.5t_3\Rightarrow 12t_2=\frac{S}{2}<br/>\end{array}<br/>$
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 $\frac{S}{t}=\frac{S}{\frac{S}{4}}=4m/s$