Question

A particle moving in a straight line covers half the distance with a speed of 3m/s. The other half of distance is covered with double speed 6m/s. The average sped of the particle is:

• A. 4.5 m/s
• B. 4 m/s
• C. 9 m/s
• D. 5 m/s

Answer 1

The correct option is B 4 m/s

Let's consider, $x=$ total distance covered by the particle

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

$t_1=\frac{x}{2\times 3}=\frac{x}{6}s$

The other half of the distance is covered with speed $6m/s$, then

$t_2=\frac{x}{2\times 6}=\frac{x}{12}s$

Total time, $t=t_1+t_2$

$t=\frac{x}{6}+\frac{x}{12}=0.25xs$

The average speed of the particle is

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

$v_{avg}=4m/s$

The correct option is B.