Question

Explain how speed is a rate of change?

Answer 1

Hint: As we know that speed of the body is nothing but the ratio of distance covered by the body in a unit interval of time, as speed is the ratio of distance and time, so we can say that it is nothing but simply denoting the rate with which the body is changing its distance or places.

Complete Step by Step Solution:
As we know that,
Speed of body is nothing but the ratio of distance covered by body to the time taken by body to covering that particular distance.
Means, rates give us a simple brief about the motion of the body that how much distance it is covering in a particular span of time interval.
Speed \[=\] Distance/ Time
Here, time is base quantity, so speed can be defined by distance travelled by body in a unit interval of time span.
As here we have to justify hoe speed is called the rate of change.
As we know that,
Rate means nothing but change per unit time.
In general, if we write \[5\,Kmph\] here, it simply means that the body travels \[5\text{ }Km\]in one Hr. or we can say that the body covers a distance of \[5\text{ }Km\]in each and every hour.
So, speed is nothing but simply the distance covered by the body in a unit interval of time.
Word “Rate of change” means that it continuously changes with base quantity.

Additional information:
Speed of a system is generally denoted in two different quantities.one is \[Km/Hr\]. and another is m/sec.
When we need to convert\[Km/Hr\]. In m/sec we need to multiply the value of speed by \[5/18\] while when we need to convert m/sec in \[Km/Hr\]. we need to multiply the value by \[18/5\].
Hence, by multiplying the values by \[5/18\] or \[18/5\] we can convert the speed from one quantity to another quantity.

Note:
As speed is nothing but distance travelled in the unit interval of time, so we can say that the body is changing its position with changing in the value of time, so we can say that speed is changing with time, or it is the rate of change of time.
Speed may be in \[Km/Hr\]or m/sec, if it is in \[m/\sec \]it means by it is denoting the distance in \[''m''\] covered by the body in one second.