Question

An insect crawling straight down the length of a meter stick is at the 12-cm mark at one instant, and 2 minutes later is at the 60-cm mark.
Which of the following is the magnitude of the insect’s velocity?
$\eqalign{
  & {\text{A}}{\text{. }}0.4cm/s \cr
  & {\text{B}}{\text{. }}0.5cm/s \cr
  & {\text{C}}{\text{. }}24cm/s \cr
  & {\text{D}}{\text{. }}30cm/s \cr} $

Answer 1

Hint: We are provided with the initial and final position of the insect, using that to calculate the displacement of the insect. Then substitute its value in the formula of velocity with the given time interval to calculate the required answer.

Formula used:
$\overrightarrow v = \dfrac{{\overrightarrow s }}{t}$

Complete step by step answer:
The magnitude of the displacement of a particle is calculated as the length of the straight line joining the initial position to the final position of the particle. And its direction is taken from the initial position to the final position. Thus displacement has both magnitude and direction, so it is a vector quantity. It is denoted by $\overrightarrow s $.
The velocity of a particle is defined as its displacement divided by the time interval in which that displacement was achieved. It is a vector quantity, which means it has direction as well as magnitude associated with it. It is denoted by $\overrightarrow v $.
Mathematically, velocity can be written as:
$\overrightarrow v = \dfrac{{\overrightarrow s }}{t} \cdots \cdots \cdots \cdots \cdots \left( 1 \right)$
where t represents the time interval.
Given in question:
Initial position of the insect on the meter scale: 12 cm
Final position of the insect on the meter scale: 60 cm
Time interval in which the distance is covered, t= 2 minutes $ = 2 \times 60\sec = 120{\text{ seconds}}$
So, the magnitude of Total Displacement of the insect = Final position – Initial position
$\eqalign{
  & \left| {\overrightarrow s } \right| = 60 - 12cm \cr
  & \Rightarrow \left| {\overrightarrow s } \right| = 48cm \cr} $
Now, the magnitude of insect’s velocity will be given by equation (1), so we have:
$\eqalign{
  & \left| {\overrightarrow v } \right| = \left| {\dfrac{{\overrightarrow s }}{t}} \right| \cr
  & \Rightarrow \left| {\overrightarrow v } \right| = \dfrac{{\overrightarrow {\left| s \right|} }}{t} \cr
  & \Rightarrow \left| {\overrightarrow v } \right| = \dfrac{{48cm}}{{120\sec }} \cr
  & \therefore \left| {\overrightarrow v } \right| = 0.4cm/\sec \cr} $
Therefore, the correct option is A, i.e. the magnitude of the insect’s velocity is 0.4cm/sec.

Note:
The magnitude of velocity is nothing but the scalar absolute value of velocity, which otherwise is known as speed. Its SI unit is meter per second or m/sec and CGS unit is centimeter per second or cm/sec. Students must not be confused if the question is asked as to what is the speed of the insect.