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 $=\frac{1}{2}\times 10\times 15=75$ For B, area $=10\times 15=150$

Segment C is a trapezium whose area is, $\frac{1}{2}\times (\text{sum of parallel sides})\times \text{height}$

For C, area $=\frac{1}{2}\times (15+25)\times 10=200$ For D, area $=\frac{1}{2}\times 20\times 25=250$

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