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 interval 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. $5.0m/s$
• C. $5.5m/s$
• D. $4.8m/s$

Answer 1

The correct option is (A) $4.0m/s$

Given,

The particle is covering half of the distance with 3 m/s

Other half distance in two equal time intervals with speed of 4.5 m/s and 7.5 m/s

Let the total distance traveled by the particle is S

So,

Time taken by the particle for the first half distance ($t_1$)

$t_1=\frac{\frac{S}{2}}{3}=\frac{S}{6}$

According to the question second half distance is traveled in two equal time time intervals

So,

Let time interval be t

We can write,

$\frac{S}{2}=4.5\times t+7.5t\Rightarrow 12t=\frac{S}{2}$

Or, $t=\frac{S}{24}$

Now,
Total time $t=t_1+t+t=\frac{S}{6}+\frac{S}{24}+\frac{S}{24}=\frac{S}{4}$

We know,

$Averagespeed=\frac{Totaldistancetraveled}{Totaltimetaken}$

So,
Average = $\frac{S}{t}=\frac{S}{\frac{S}{4}}=4m/s$

Hence, the average speed is 4 m/s