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...... $\,m/s$
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...... $\,m/s$
$4$
$5$
$5.5 $
$4.8$
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...... $\,m/s$
If ${t_1}$ and $2{t_2}$ are the time taken by particle to cover first and second half distance respectively.
${t_1} = \frac{{x/2}}{3} = \frac{x}{6}$…(i)
${x_1} = 4.5\;{t_2}$ and ${x_2} = 7.5\;{t_2}$
So, ${x_1} + {x_2} = \frac{x}{2} \Rightarrow 4.5{t_2} + 7.5{t_2} = \frac{x}{2}$
${t_2} = \frac{x}{{24}}$…(ii)
Total time $t = {t_1} + 2{t_2} = \frac{x}{6} + \frac{x}{{12}} = \frac{x}{4}$
So, average speed $ = 4\;m/sec$.
Other Language