Question

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 \( 0.8 \, {m/s} \) at \( x = 0 \), then its velocity at \( x = 1.4 \, {m} \) is: \includegraphics[]{83.png}

• A. \( 1.6 \, {m/s} \)
• B. \( 1.2 \, {m/s} \)
• C. \( 1.4 \, {m/s} \)
• D. \( 0.8 \, {m/s} \)

Hint:

When working with position and acceleration graphs, calculate the area under the curve to determine the change in velocity.

Answer 1

The Correct Option is B

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 \( 0.8 \, {m/s} \), 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 \( 1.2 \, {m/s} \) at \( x = 1.4 \).
Thus, the velocity at \( x = 1.4 \, {m} \) is: \[ \boxed{1.2 \, {m/s}} \]