You know that the force applied on a body is directly proportional to the acceleration produced in the body. Write an equation to express this situation and plot the graph of the equation.
You know that the force applied on a body is directly proportional to the acceleration produced in the body. Write an equation to express this situation and plot the graph of the equation.
Here the variables involved are force and acceleration. Let the force applied be $y$ units and the acceleration produced be $x$ units. From ratio and proportion, you can express this fact as $y = kx$, where $k$ is a constant. (From your study of science, you know that $k$ is actually the mass of the body.)
Now, since we do not know what $k$ is, we cannot draw the precise graph of $y = kx$. However, if we give a certain value to $k$, then we can draw the graph. Let us take $k = 3$, i.e., we draw the line representing $y = 3x.$
For this we find two of its solutions, say $(0,\, 0)$ and $(2,\, 6)$ (see Fig.).
From the graph, you can see that when the force applied is $3$ units, the acceleration produced is $1$ unit.Also, note that $(0,\, 0)$ lies on the graph which means the acceleration produced is $0$ units, when the force applied is $0$ units.
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In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius :
$F =\left(\frac{9}{5}\right) C +32$
$(i)$ Draw the graph of the linear equation above using Celsius for $x$ - axis and Fahrenheit for $y$ - axis.
$(ii)$ If the temperature is $30\,^oC$, what is the temperature in Fahrenheit ?
$(iii)$ If the temperature is $95\,^oF$, what is the temperature in Celsius ?
$(iv)$ If the temperature is $0\,^oC$ , what is the temperature in Fahrenheit and if the temperature is $0\,^oF$ , what is the temperature in Celsius ?
$(v)$ Is there a temperature which is numerically the same in both Fahrenheit and Celsius ? If yes, find it.
In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius :
$F =\left(\frac{9}{5}\right) C +32$
$(i)$ Draw the graph of the linear equation above using Celsius for $x$ - axis and Fahrenheit for $y$ - axis.
$(ii)$ If the temperature is $30\,^oC$, what is the temperature in Fahrenheit ?
$(iii)$ If the temperature is $95\,^oF$, what is the temperature in Celsius ?
$(iv)$ If the temperature is $0\,^oC$ , what is the temperature in Fahrenheit and if the temperature is $0\,^oF$ , what is the temperature in Celsius ?
$(v)$ Is there a temperature which is numerically the same in both Fahrenheit and Celsius ? If yes, find it.