Question

If the unit of length is micrometer and the unit of time is microsecond, then the unit of velocity will be:
a) 100m/s
b) 10m/s
c) Micrometers
d)m/s

Answer 1

Hint: In the above question the unit of length is given to us as micrometer and that of time is given as microsecond. Velocity of any body is defined as the displacement of the body per unit time such that the body moves with constant velocity. Hence using the above relation we can obtain the unit of velocity in terms of units of velocity and time.
Formula used:
$v={\displaystyle \frac{s}{t}}$

Complete answer:
Let us say the particle gets displaced from its initial position such that its net displacement is ‘s’. If the body was moving with a constant velocity ‘v’ and the time taken by the body to get displaced by ‘s’ was ‘t’, than the velocity of the body is given by,
$v={\displaystyle \frac{s}{t}}$
In the question the unit of length covered is given as micrometer and that of time is given as microsecond. The micro is a multiplier of ten to the power of negative six. Hence using the above equation, the units of velocity is equal to
$\begin{array}{rl}& v={\displaystyle \frac{s}{t}}\\ & \Rightarrow v={\displaystyle \frac{{10}^{-6}m}{{10}^{-6}s}}\\ & \therefore \Rightarrow v={\displaystyle \frac{m}{s}}\end{array}$

Therefore the correct answer of the above question is option d.

Note:
It is to be noted that if a body covers some distance which is equal to the same interval of time i.e. if the magnitude is the same, the velocity of the particle or a body will always be equal to one meter per second. No matter how big or small is the path covered, if the magnitude of the time interval is the same, the unit of velocity will be in most general form SI units.