Simple Problem on Speed-Time Graph II
When a body is in motion, it moves with certain speed
Speed can be defined as the rate of change of distance with respect to time
We usually represent speed as a function of time graphically
This graph is known as the speed-time graph, where speed is taken along the
$y$
- axis and time along the
$x$
axis
Speed-Time graph is usually used to calculate the distance travelled by a body
When we plot speed of a body at different periods of time, then we get a speed-time curve
By finding the area under the curve we get the distance travelled by the body
Let us study different type of curves of a Speed-Time graphs
When the speed of the body is constant, the curve is given by a straight line parallel to the time axis
Now when the speed of the body increases uniformly, the curve is given by a straight line starting from the origin
When the speed of the body decreases, the curve will be similar to the one shown in the image
In all these cases, the area under the curve gives the distance travelled by the body
Let us solve a problem based on the speed-time graph
The above graph represents
$50$
seconds of a car's journey
Work out the total distance travelled by the car in
$50$
seconds
We learnt that, for a speed-time graph, the distance travelled is the area under the graph. So let us calculate the area under the curve
To work out the area under this graph, we will break it into 4 segments: A, B, C and D
For A, area
$=21â€‹Ã—10Ã—15=75$
For B, area
$=10Ã—15=150$
Segment C is a trapezium whose area is,
$21â€‹Ã—(sumÂ ofÂ parallelÂ sides)Ã—height$
For C, area
$=21â€‹Ã—(15+25)Ã—10=200$
For D, area
$=21â€‹Ã—20Ã—25=250$
Therefore, total area
$=75+150+200+250=675m_{2}$
Hence, the total distance travelled by the car during
$50$
seconds is
$675$
$m$
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 same as 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