Question

Question 6
The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to 6 kg. Read from the graph, the force required when the acceleration produced is:
(i) $5m{s}^{-2}$
(ii) $6m{s}^{-2}$

Answer 1

Given that force (F) is directly proportional to the acceleration (a).
i.e F $\propto$ a
$\Rightarrow$ F = ma [ where, m = arbitrary constant and take value 6kg of mass]
$\therefore$ F = 6a ....(i)

(i) If $a=5m/s^2$, then from Eq.(i); we get,
$\Rightarrow F=6\times 5=30N$

(ii) If $a=6m/s^2$, then from Eq.(i) we get
$\Rightarrow F=6\times 6=36N$

Here, we find two point A(5, 30) and B(6, 36).
Hence, the graph can be plotted by plotting the points A and B and joining the line AB.