Measuring Speed

Introduction to measuring speed:

We all are familiar about speed.Speed is the distance covered by time.We used to tell about the speed of car (say) by how long it traveled within the unit time.

Usually miles/hr ,km/hr ,meter/sec etc.The difference between two objects traveling at different speeds is the distance covered by them within the unit time.

So ,we can tell that speed is directly proportional to the distance and it is inversely proportional to the time.

So that s=d/t

Where s is the speed ,d  the distance, and t the time.

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An Example for Measuring Speed

Suppose we are driving a car from new York to Boston.

Let the distance between those two are 300 km.And one took 4 hours to reach.

Now ,we can calculate the speed of the journey

Speed v=distance covered s/time taken t

So v=300/4

V=75km/hr

So the speed is the rate of change with time

But,can we tell this was the speed of the car,all the way..?

No! it will be the speed ,if the speed was same all along the way.

But there is only rare chance for it.

So we can tell what we found was the average speed of the journey.

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Measuring Instantaneous Speed

Instantaneous speed:

As all of us know,the speedometer of the car shows the speed at the particular time.

We can tell this speed as the instantaneous speed of the car.

To find the instantaneous speed ,we can seek the help of calculus.

The instantaneous speed of the car is the first derivative of the distance wrt time.

For this we are taking a limit of the time ,as it tends to 0

So v=lim `Delta` t  -->0   `Delta` v/`Delta` t  (read as delta v/ delta t)

V=ds/dt in terms of derivative.

Another way to find instantaneous speed:

We can find the speed also by the distance –time graph

The speed is the slope of the line in distance time graph.