Question

A particle moving along a straight line covers half of the distance with a speed of $3{ms}^{-1}$. The other half of the distance is covered in two equal time intervals with speed of $4.5{ms}^{-1}$ and $7.5{ms}^{-1}$. The average speed of the particle (in ${ms}^{-1}$) is

• A. $5.0$
• B. $5.5$
• C. $5.8$
• D. $4.0$
• E. $4.8$

Answer 1

The correct option is D $4.0$

Let the total distance covered by the particle be $S$. Given that, particle covers $\frac{S}{2}$ with a speed of $3m/s$.

The time taken to cover this distance is, $t_1=\frac{\frac{S}{2}}{3}$

or, $t_1=\frac{S}{6}$

Let the time taken to complete the other half distance be $2t_2$. We have,

$t_2\times 4.5+t_2\times 7.5=\frac{S}{2}$

or, $12t_2=\frac{S}{2}$

or, $t_2=\frac{S}{24}$

The average speed $v_{avg}=\frac{totaldistance}{totaltime}$

or, $v_{avg}=\frac{S}{t_1+t_2}$

Using $t_1=\frac{S}{6}$ and $t_2=\frac{S}{24}$, we get,

$v_{avg}=\frac{S}{\frac{S}{6}+\frac{S}{24}}$

or, $v_{avg}=4m/s$, is our required answer.