Question

A particle moving in a straight line covers half the distance with speed of $3m/s$. The other half 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. $5.5m/s$
  
• C. $4.8m/s$
  
• D. $5.0m/s$
  

Answer 1

The correct option is A $4.0m/s$


Given,
A particle moving in a straight line covers half the distance in time $t_1$ and other half distance in two equal time $t_2.$
$t_1=\frac{\frac{x}{2}}{3}=\frac{x}{6},$
$x_1=4.5t_2,$
$x_2=7.5t_2$
Also $x_1+x_2=\frac{x}{2}=(4.5+7.5)t_2$
$t_2=\frac{x}{24}$
Total time$t=t_1+2t_2=\frac{x}{6}+\frac{2x}{24}=\frac{x}{4}$
$v_{a}v=\frac{x}{t}=4m/s$

Final Answer: (𝑎)