Simple Problem on Speed-Time Graph

We can write the speed of a body as a function of time

We can do so by plotting the speed of a body at different times in a graph

This graph is known as Speed-Time graph, with speed in $y$ - axis and time in $x$ - axis

There are some concepts related to a speed-time graph

Let us study these concepts

The area under the curve gives us the distance travelled by the body, i.e. $area under curve = s$ , distance

Now there can arise three general cases for which we get different curve of the speed-time graph

Case 1: When the body moves with a constant speed, the curve will be a straight line parallel to time axis as shown

In this case 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 similar to the image shown above

In this case also, the area under the curve will give us 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 image shown above

The area under the curve gives us the distance moved by the body over a period of time

Let us try to solve a simple problem based on these concepts

From the above Speed-time graph, calculate the total distance travelled by the body from $0$ to $30$ seconds

To find the distance we need to find out the area under the curve

As, distance travelled = sum of all the areas of the segments under the curve (as shown in the graph)

For OAE, area $= \frac{1}{2} \times 10 \times 10 = 50$ For EABD, area $= \frac{1}{2} \times (10 + 30) \times 10 = 200$

And for BCD, area $= \frac{1}{2} \times 30 \times 10 = 150$

Total area under the curve = $50 + 200 + 150 = 400$

Hence total distance travelled by the body is $400$ $m$

Revision

Speed-Time graph gives the relation between speed and time of a body, with speed in $y$ - axis and time in $x$ - axis

When the speed is constant, the curve will be a straight line parallel to time axis

When the speed is uniformly increasing, the curve will be similar to the one shown in the image

When the speed is uniformly decreasing, the curve will be similar to the one shown in the image

For all the cases, the area under the curve will give us the distance travelled by the body

The End