Question

A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half 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

The correct option is A 4.0 m/s

if $t_1$ and $2t_2$ are the time taken by particle to cover first and second half distance respectively.
$t_1=\frac{\frac{x}{2}}{3}=\frac{x}{6}...\left(i\right)$
$x_1=4.5t_2$ and $x_2=7.5t_2$
so, $x_1+x_2=\frac{x}{2}\Rightarrow 4.5t_2+7.5t_2=\frac{x}{2}$
$t_2=\frac{x}{24}...\left(ii\right)$
Total time $t=t_1+2t_2=\frac{x}{6}+\frac{x}{12}=\frac{x}{4}$
so average speed = 4m/sec.