Basic Knowledge of Distance - Time Graph

We all love to watch a game of cricket.

If you ever noticed during the break, various graphs appear on the screen.

They give us information about run-rate, partnerships etc., and we can understand them very easily.

In this way, graphs convey information in a very convenient manner.

We can use this knowledge of graphs to understand the relationship between different variables like distance and time.

Let’s understand distance-time graphs.

Distance gives us an idea of how far two points are situated. And to cover this distance we require time.

And while representing them in a graph, we usually take time in the $x - a x i s$ and distance is taken in the $y - a x i s$ .

This graph will give us simple information. "Where the body is at a given time". As the above graph shows, the body is at 100 units distance, at time 2 units.

The above graph shows that the body is at the same distance at all times. This means that the body is not moving at all.

Let’s learn to plot graphs for different kinds of motion.

If the object is moving with a uniform speed, that means it is covering equal distances in equal intervals of time.

Since the object is covering equal distances in equal intervals of time, the graph will be a straight line. And the graph would look like this.

Let’s try to plot the distance-time graph with a car, watch and an odometer.

Consider a car is moving. We have a watch to measure the time and an odometer in the car to measure the distance.

We start our journey at 8:00 AM, let's say the odometer is reading 36540 km at the beginning. We note the odometer reading every half an hour.

The last column is to measure the distance travelled. Like at 8:30AM distance traveled is $(36560 - 36540)$ = $20 k m$ . At 9:00 AM it is $(36580 - 36540)$ = $40 k m$ . And so on.

Let's take 8:00 AM as 0, 8:30 AM as 30mins, 9:00 AM as 60 mins, and so on. So the x-axis and y-axis before we plot the graph look like this.

So the points plotted above show that at 30min the car is at 20km, at 60mins the car is at 40km, and at 90min the car is at 80km and so on. We know that car travelled 0km at 0 minutes.

So if we join the points to make a line the graph looks like this.

We can find the speed of a car from the graph.

In this graph we can find speed by dividing the distance and time take. The car went a distance $S_{1}$ to $S_{2}$ = $40 - 10 = 30 k m$ in $(60 - 40) = 20 m i n$

So the speed is the ratio of Distance and time. So the $s p e e d = 30 k m / 20 m i n = 1.5 k m / m i n$ after conversion of minute into hours we get speed = $90 k m / h r$

If our speed is constantly changing with time, and we moving in non-uniform motion. Then this is how the graph for distance-time wont be a straight line.

We will discuss more about distance - time graphs for non-uniform motion later.

Let’s have a small revision of what we have learned.

Graphs help us in conveying the information very conveniently. Using graphs in finding a distance-time relationship is often very effective.

Graphs tell us the nature of the motion of an object. And we can calculate the speed from the graph itself.

The End