Question

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 $6kg$. 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 $\left(F\right)$ is directly proportional to the acceleration $\left(a\right)$.
i.e $F\propto a$
$\Rightarrow F=ma$ [ where, $m$ is an 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 found 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 $AB$.