Question

A body covers first $\frac{1}{3}$ part of its journey with a velocity of 2 m/s, next $\frac{1}{3}$ part with a velocity of 3 m/s and rest of the velocity 6 m/s. The average velocity of the body will be

• A. 3 m/s
• B. $\frac{11}{3}$ m/s
• C. $\frac{8}{3}$ m/s
• D. $\frac{4}{3}$ m/s

Answer 1

Answer: (A)

3 m/s

Let the total distance = 3x,
The travel takes place in 3 parts:
x distance at $2m{s}^{-1}$
x distance at $3m{s}^{-1}$
x distance at $6m{s}^{-1}$
The time taken in each individual travel is:
$t_1=\frac{x}{2}$
$t_2=\frac{x}{3}$
$t_3=\frac{x}{6}$
Hence the total time taken is :
$t_1+t_2+t_3=x$
Total distance travelled = $3x$
Average velocity $=\frac{3x}{x}=3m{s}^{-1}$
Hence option A is correct.