The acceleration of a particle which moves along the positive \( x \)-axis varies with its position as shown in the figure. If the velocity of the particle is \( 0.8 \, \text{m/s} \) at \( x = 0 \), then its velocity at \( x = 1.4 \, \text{m} \) is:
Show Hint
When working with position and acceleration graphs, calculate the area under the curve to determine the change in velocity.
The velocity of the particle can be found using the work-energy theorem, which relates the change in velocity to the area under the acceleration versus position curve. Given that the velocity at \( x = 0 \) is \( 0.8 \, \text{m/s} \), and from the graph, the area under the curve between \( x = 0 \) and \( x = 1.4 \) is the work done, which contributes to the change in velocity. From the graph, we can estimate the area, which leads to a velocity of \( 1.2 \, \text{m/s} \) at \( x = 1.4 \). Thus, the velocity at \( x = 1.4 \, \text{m} \) is: \[ \boxed{1.2 \, \text{m/s}} \]
