Question

A particle moving in a straight line covers half the distance with a speed of 3 m/s. The other half of the distance is covered in two equal time intervals with uniform speeds of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is

Answer 1

Lets consider, $x=$ total distance covered by a particle

Half of the distance is covered with speed $3m/s$, then time required to covered the distance is

$t_1=\frac{x}{6}sec$

Other half of the distance is covered in two equal time interval with uniform speed $4.5m/s$ and $7.5m/s$ respectively

Then time required is

$t_2=\frac{x}{4\times 4.5}=\frac{x}{18}sec$

And $t_3=\frac{x}{4\times 7.5}=\frac{x}{30}sec$

Total time required , $t=t_1+t_2+t_3$

The average speed of the particle during the motion is

$v_{avg}=\frac{Totaldistancecovered}{Totaltime}$

$v_{avg}=\frac{x}{t}$

$v_{avg}=\frac{x}{t_1+t_2+t_3}$

$v_{avg}=\frac{x}{\frac{x}{6}+\frac{x}{18}+\frac{x}{30}}$

$v_{avg}=\frac{x}{0.25x}$

$v_{avg}=4m/s$

The correct option is D.