A particle is moving with constant acceleration $$a$$. Following graph shows $$v^2$$ versus $$x$$ (displacement) plot. The acceleration of the particle is _________ m s$$^{-2}$$.

$$\text{From the third equation of motion: } v^2 = u^2 + 2ax$$

$$\text{Comparing this expression with the equation of a straight line, } y = mx + c\text{, where } y = v^2 \text{ and } x = x:$$

$$\text{Slope } (m) = 2a \implies a = \frac{\text{Slope}}{2}$$

$$\text{Determine the slope using the data coordinates from points } A(10, 40) \text{ and } B(20, 60)\text{:}$$

$$\text{Slope } (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{60 - 40}{20 - 10} = \frac{20}{10} = 2\text{ m/s}^2$$

$$a = \frac{m}{2} = \frac{2}{2} = 1\text{ m s}^{-2}$$