Question

How do you convert $ 8pm{(\mu s)^{ - 1}} $ to $ m{s^{ - 1}} $ ?

Answer 1

Hint :Velocity has the S.I. unit of $ m{s^{ - 1}} $ . It is a quantity used to represent how fast or how slow an object is moving along a certain direction, thus it is a vector quantity which is relative in nature depending on the point where the viewer is viewing from in space.

Complete Step By Step Answer:
To do the above conversions we first need to know what a $ pm $ (Picometer) amounts to, how much in meters $ m $ and similarly what a $ \mu s $ (microseconds) amounts to in seconds $ s $ .
 $ 1picometre\left( {pm} \right) = {10^{ - 12}}metre\left( m \right) $
Similarly, $ 1\mu s = {10^{ - 6}}s $
Thus, $ 1pm{(\mu s)^{ - 1}} = {10^{ - 12}}m{(\mu s)^{ - 1}} $
 $ = \dfrac{{{{10}^{ - 12}}m}}{{{{10}^{ - 6}}s}} = {10^{ - 12 + 6}}m{s^{ - 1}} = {10^{ - 6}}m{s^{ - 1}} $
So, $ 8pm{(\mu s)^{ - 1}} = 8 \times {10^{ - 6}}m{s^{ - 1}} $ which is the required answer.

Additional Information:
Kinematics is the study of objects in motion and the basic pillars in kinematics are Acceleration, Velocity, Position and Jerk.
Position of an object is the destination where we find an object in space.
Velocity is defined as the change in position of an object with time along a certain direction which needs to be specified due to the vector or directional nature of velocity.
Acceleration is defined as the rate of change in velocity with time, It gives us an idea about how far an object would reach if it has an ever changing velocity in space, It has a value of zero if an object does not move at all or moves but only at a constant velocity.
Jerk is the rate of change in acceleration with time and it helps in understanding how haphazard the motion of a particle is in space.
Knowing above parameters we can get a near complete idea on where the object could be after a certain amount of time has passed.

Note :
When converting values from one unit to another we need to be highly careful about what conversion factors we use as even the tiniest mistake in conversion factor could change the whole answer and develop a great error. That being said, always be careful about mentioning the units in every step after the magnitude whenever you do a conversion.