Speed-Time Graph

Graphs are used to show how things are related to each other

Graphs give us pictorial representation of data

There are mainly three types of graphs, namely, line graph, bar graph and pie graph

Line graphs are used when two parameters have to be compared with respect to each other

Pie graphs are used to compare different sections of a single parameter

Bar graphs are usually used to compare items between different groups and track changes over a period of time.

Speed and time are two different quantities. But using graphs we can represent the variation of one with respect to the other

Let us see how we can graphically represent speed as a function of time

The graph which represents the change of speed over time is known as the Speed-Time graph

In a speed-time graph, speed is always plotted on the vertical axis (i.e. $y$-axis) whereas, time is plotted on the horizontal axis (i.e. $x$-axis)

Speed time graph gives us information regarding the distance travelled by a body

When we plot speed of a body for different periods of time, we get a curve

The area under this curve gives us the distance travelled by the body

Let us prove this result using a speed-time graph of a body

Let us consider a speed time graph as shown above

Then, the area of the shaded region will be the sum of the rectangle AODC and the triangle ABC

That is, Shaded area = area of rectangle AODC + area of triangle ABC$\Rightarrow (\text{length}\times \text{ breadth})+(\frac{1}{2}\times \text{base}\times \text{height})$

Putting the values from the graph, we get, Area $=(u\times t)+(\frac{1}{2}\times (v-u)\times t)$

Simplifying the last term, we will get,Area $=\frac{(u+v)}{2}t$

Where, $\frac{u+v}{2}$ is the average speed and $t$ is the time. And we know, distance is equal to the product of the speed and time

Therefore, Area $=\frac{(u+v)}{2}t=s$Where, $s$ is the distance travelled by the body

Usually we have 3 kinds of speed time graphs

Case 1: If the speed of a body is constant over a period of time, then the curve will be straight line parallel to time axis

And the area under the curve gives the distance travelled by the body

Case 2: If the speed of a body uniformly increases from zero with time, then the curve will be as shown in the image

Here also the area under the curve gives the distance travelled by the body

Case 3: When the speed of the body decreases from non zero value to zero, the curve will be similar to the above image

For this case also the area under the curve gives the distance travelled

Revision

In a speed-time graph, speed is always plotted on the vertical axis (i.e. $y$-axis) whereas, time is plotted on the horizontal axis (i.e. $x$-axis)

When we plot speed of a body for different periods of time, we get a curve

The area under this curve gives us the distance travelled by the body

If the speed of a body is constant for a period of time, then the curve will a straight line parallel to time-axis

If the speed of a body uniformly increases from zero with time, then the curve will be as shown in the image

When the speed of the body decreases from non zero value to zero, the curve will be similar to the one shown in image

For all cases, the area under the curve gives the distance travelled by the body

The End