Question

A particle covers half the total distance with speed of $3\,m/s$ . The rest of the distance is covered in two equal time intervals with speed of $4.5\,m/s$ and $7.5\,m/s$ respectively. The average speed of the particle during this motion is:-

• A. $4.0\,m/s$
• B. $5.0\,m/s$
• C. $5.5\,m/s$
• D. $4.8\,m/s$

Answer 1

Answer: (A)

If $t_{1}$ and $2t_{2}$ are the time taken by particle to cover first and second half distance respectively $t_{1}=\frac{x / 2}{3}=\frac{x}{6}\ldots .\left(\right.i\left.\right)$
$x_{1}=4.5t_{2}$ and $x_{2}=7.5t_{2}$
So, $x_{1}+x_{2}=\frac{x}{2}\Rightarrow 4.5t_{2}+7.5t_{2}=\frac{x}{2}...\left(i i\right)$
Total time $t=t_{1}+2t_{2}=\frac{x}{6}+\frac{x}{12}=\frac{x}{4}$
So, average speed $=4\,m/sec$