Question

Aarushi was driving a car with a uniform speed of 60 kmph. Draw distance time graph from the graph to find the distance travelled by Aarushi. distance travelled by Aarushi in
(1) $2\dfrac{1}{2}$ hour
(2) $\dfrac{1}{2}$ hour

Answer 1

Hint : Here the question seems to be a physics question but it is a mathematics question. The question is related to the graph concept. By reading the question we have to write the equation which contains the variables x and y. The x represents the distance and y represents the time. Hence by analysing the graph we can determine the solution for the given question.

Complete step by step solution:
A graph of a function is a set of ordered pairs and it is represented as $y = f(x)$ , where x and f(x) are real numbers. These pairs are in the cartesian form and the graph is the two-dimensional graph.
Now let us consider the question, in the question they have mentioned the words speed, distance and time.
In a physics we have a formula which is related to these parameters, that is given by
Distance = speed $\times$ time. --- (1)
Let we consider the distance as x and the time as y.
From the question, we know the value of speed. The speed = 60 kmph.
Substituting the values in the equation (1) we have
$\Rightarrow x = 60 \times y$
This can be written as
$\Rightarrow x = 60y$
Now here we give the values for the y and determine the value of x.
So we have

x	0	60	120
y	0	1	2

Now we will plot a graph for the above points

Now we have to determine the distance travelled by Aarushi in $2\dfrac{1}{2}$ hour and $\dfrac{1}{2}$ hour. From the graph we will determine this.
On the y axis we will mark the time and take a dotted line, the dotted line will touch the graph line of the function. From that point we draw a perpendicular line to the x axis. Hence we determine the distance.
For $2\dfrac{1}{2}$ hour, we mark 2.5 on y axis and take a dotted line, the dotted line will touch the graph line of the function. From that point we draw a perpendicular line to the x axis
Therefore the distance travelled by Aarushi in $2\dfrac{1}{2}$ hour is 150 km.
For $\dfrac{1}{2}$ hour, we mark 0.5 on y axis and take a dotted line, the dotted line will touch the graph line of the function. From that point we draw a perpendicular line to the x axis
Therefore the distance travelled by Aarushi in $\dfrac{1}{2}$ hour is 30 km.

Note : The graph is plotted x-axis versus y axis. The graph is two dimensional. By the equation of a graph, we can plot the graph by assuming the value of x. We can’t assume the value of y. because the value of y depends on the value of x. Hence, we have plotted the graph. If we go wrong in drawing a straight line, then our answer will be wrong.