Question

A body of mass m moving along a straight line covers half the distance with a speed $2m{s^{ - 1}}$ The remaining half of the distance is covered in two equal time intervals with a speed of $3m{s^{ - 1}}$ and $5m{s^{ - 1}}.$ The average speed of the particle
for the entire journey is

A.)$\dfrac{3}{5}m{s^{ - 1}}$
B.)$\dfrac{8}{3}m{s^{ - 1}}$
C.)$\dfrac{4}{3}m{s^{ - 1}}$
D.)$\dfrac{{16}}{3}m{s^{ - 1}}$

Answer 1

Hint: This question is from the chapter of kinematics where we basically deal with the dimension motion of any objects like its speed ,distance covered, time taken to cover any distance ,its acceleration etc. In this chapter we don’t deal with the cause of motion i.e. force.

Complete step-by-step answer:
Given

Speed to cover half distance is $2m{s^{ - 1}}$
And the remaining distance with a speed $3m{s^{ - 1}}$ and $5m{s^{ - 1}}.$
Let the total distance travelled by the body be 2S
Also, the time taken by the body to travel first half be ${t_1}$

Therefore

${t_1} = \dfrac{S}{2}$

Now, let ${t_2}$ be the time taken by the body for each time interval for the remaining half journey.

Therefore the distance of the remaining half will be

$S = 3{t_2} + 5{t_2} = 8{t_2}$

As we know that the average speed is given by

$average\,\,speed = \dfrac{{total\,distance}}{{total\,time}}$

$
   = \dfrac{{2S}}{{{t_1} + 2{t_2}}} \\
   = \dfrac{{2S}}{{\dfrac{S}{2} + \dfrac{S}{4}}} \\
   = \dfrac{8}{3}m{s^{ - 1}} \\
$

Hence, the correct option is B.

Additional Information- The goal of any study of kinematics is to develop sophisticated mental models that serve to describe (and ultimately, explain) the motion of real-world objects.

Note- In order to solve these types of questions, remember the basic definitions of the average distance and use that definition to reach the answer. As in the above question we first calculated the total distance and total time, then using the definition of average speed found the answer. Never calculate average speed by calculating the average of the speeds.