Speed and Average Speed

When we are travelling in a car when going on a holiday...

In the front near the steering wheel, we can see the speedometer changing in the car. Initially, it is at 0 then it moves to 20, 40, and so on.

The needle points towards a number, that number is nothing but the speed of the car.

Depending on the speed of the car the needle moves. And depending on the speed of the car we define different types of motions.

When a body is moving, at any instant, the speed of a body is defined as the ratio of the distance travelled by it in the instant and the length of the instant i.e time.

We calculate speed in an instant. Here, instant means a very small interval of time. An instant is comparable to 1 second or less. So it is also called instantaneous speed.

Speedometer shows only instantaneous speed.

Depending on the speed of the body, motion is divided into two types. Uniform and Non-uniform motion.

Uniform and Non-uniform motion

If the needle is showing only 20 constantly, then the speed of the car is 20 and uniform throughout the motion. This kind of motion is called $U n i f o r m$ $m o t i o n$ .

When a body is in uniform motion, then the body covers equal distances in equal intervals of time.

If the needle keeps moving, then the speed of the car is not constant. This type of motion is called $N o n - U n i f o r m$ $M o t i o n$ .

When a body is in non-uniform motion we study the motion using average speed.

Now let's learn about Average speed.

Average speed

Let's say we are going from Chennai to Delhi on the Grand trunk express.

Usually, it takes around 35 hours to travel from Chennai to Delhi.

The total distance the train had to cover is around 2024km.

In between the train stops at a few stations. It gains a speed, stops at the station and it gains speed again and again.

Now, Average Speed is defined as the ratio of the total distance travelled by the train and the time taken to cover this distance.

So the average speed by which our train has moved from Chennai to Delhi is given by $S_{a v g} = \frac{t o t a l d i s t a n c e}{t o t a l t i m e} S_{a v g} = (2024 k m) / 35 h r S_{a v g} = 57.8 k m / h r$

The meaning of Average speed is that if the train had not stopped at any station then with what uniform speed the train should have travelled to reach the destination in the same time.

Now let's see another example for calculating average speed.

A car made a 3 hours journey, the speedometer shows the speeds 30km/h,40km/h, and 50 km/h for each hour. Find the average speed.

$S_{a v g} = \frac{total distance}{total time}$ distance travelled in first hour is $D_{1}$ = $S_{1} . t i m e$ = $30 k m / h$ X $1 h$ = $30 k m$

Similarly, in second hour and third hour, the distance travelled is $D_{2}$ = $S_{2}$ X $t i m e$ = $40 k m / h$ X $1 h$ = $40 k m$ $D_{3}$ = $S_{3}$ X $t i m e$ = $50 k m / h$ X $1 h$ = $50 k m$

The average speed for the 3 hour ride is total distance by total time taken = $\frac{( D _{1} + D _{2} + D _{3} )}{total time}$ = $\frac{( 3 0 + 4 0 + 5 0 )}{3}$ km/h = $\frac{1 2 0}{3}$ km/h = $40$ km/h

Revision

The speed at an instant or the instantaneous speed is the ratio of the distance travelled in the instant and the length of the instant.

Average speed is the total distance divided by the total time. $Average Speed = \frac{Total Distance}{Time taken}$

The End