Question

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

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

Answer 1

Answer: (A)

If $t_1$ and $2t_2$ are the time taken by particle to cover first and second half distance respectively $t_1=\frac{x/2}{3}=\frac{x}{6}\dots .(i)$
$x_1=4.5t_2$ and $x_2=7.5t_2$
So, $x_1+x_2=\frac{x}{2}\Rightarrow 4.5t_2+7.5t_2=\frac{x}{2}...\left(ii\right)$
Total time $t=t_1+2t_2=\frac{x}{6}+\frac{x}{12}=\frac{x}{4}$
So, average speed $=4m/sec$