Question

How do you calculate “change in speed”?

Answer 1

Hint: In this question, we will use the basic relation between speed, distance and time. We will substitute the value of change in speed in this equation. We will also see the basic difference between speed and velocity for our better understanding.

Formula used:
$d = vt$

Complete answer:
As we know the relation between distance, speed and time is given by:
$d = vt$
$ \Rightarrow v = \dfrac{d}{t}$
Here, t is the time, d is distance and v is the speed or velocity of the object or body.

So, we have the expression to find the speed of an object or body.

Now, to find the expression for change in speed we have:
$\Delta v = {v_{final}} - {v_{initial}}$
Here, we can say that change in speed can be written as the difference in the final speed and initial speed of the object.

Now, if we put this value in above equation, we get:
$\Delta v = {\left( {\dfrac{d}{t}} \right)_{final}} - {\left( {\dfrac{d}{t}} \right)_{initial}}$
Therefore, we get the required expression to find the change in speed.

Additional information:
We already know the basic difference between speed and velocity i.e., speed is given as the measure of how fast an object can travel, whereas velocity gives us the direction of this speed. Also, speed is a scalar quantity which means that it has only magnitude, whereas velocity is a vector quantity which means that it has both magnitude and direction. The S.I unit of both speed and velocity is meter per second (m/sec).

Note:
Here, it is important to remember most speedometers have a maximum limit up to 140-160 mph. We know that the S.I unit of speed is m/sec but the speedometer shows the value in km/h. Therefore, the question can be directly solved by having an idea of the unit of speed.