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.
$areaÂ underÂ curve=s$
, 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
$=21â€‹Ã—10Ã—10=50$
For EABD, area
$=21â€‹Ã—(10+30)Ã—10=200$
And for BCD, area
$=21â€‹Ã—30Ã—10=150$
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