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 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

Let x be the total distance According to question

$\frac{x}{2}$ is covered with 3 m/s
$x_1$ is covered with 4.5 m/s
$\frac{x}{2}-x_1$ with 7.5 m/s
Let, the first $\frac{x}{2}$ is covered in $t_1$.
Also, $x_1$ and $\frac{x}{2}-x_1$ are covered in equal time ($t_2$).

$\therefore$ total time t = $t_1+2t_2$ ...(i)
and $\frac{x}{2}=3t_1$ ...(ii)
$x_1=4.5t_2$ ...(iii)
$\frac{x}{2}-x_1=7.5t_2$ ...(iv)

Adding (ii), (iii), and (iv)
$x=3t_1+(4.5+7.5)t_2$
$=3t_1+12t_2$ ...(v)

also from (iii) & (iv)
$\frac{x}{2}=12t_2$ ..(vi)

from (ii) & (v)

$12t_2=3t_1$

$\Rightarrow t_1=4t_2$ ...(vii)

from (vii), (v) and (i)

Average speed = $\frac{x}{t}$
= $\frac{3t_1+12t_1}{t_1+2t_2}$
= $\frac{24t_2}{6t_2}=4m/s$