The velocity ($v$) – distance ($x$) graph is shown in the figure. Which graph represents acceleration ($a$) versus distance ($x$) variation of this system?

Question

A 10 $\mu\text{C}$ charge is placed in an electric field of $ 5 \times 10^3 \text{N/C} $. What is the force experienced by the charge?

Answer 1

To find the correct acceleration ($a$) versus distance ($x$) graph, we need to analyze the given velocity ($v$) versus distance ($x$) graph.

Understanding the Graph:
- The velocity ($v$) vs. distance ($x$) graph shows a straight line with a negative slope.
- This indicates that velocity decreases linearly with distance.
Relation between Velocity, Acceleration, and Distance:
- From physics, we know that acceleration ($a$) is the derivative of velocity with respect to time ($t$): $a = \frac{dv}{dt}$.
- In terms of distance ($x$), acceleration can also be expressed as: $a = v \frac{dv}{dx}$.
Applying the Formula:
- Given that the velocity ($v$) is decreasing linearly with distance ($x$), the expression $ \frac{dv}{dx} $ is a constant negative value (slope of the line).
- Thus, the acceleration $a = v \frac{dv}{dx}$ also depends on $v$, which is linearly decreasing. Therefore, acceleration is linearly decreasing and negative, which relates to option A.

The correct graph for acceleration ($a$) versus distance ($x$) variation is option A, where the acceleration is linearly decreasing.

The velocity (\(v\)) – distance (\(x\)) graph is shown in the figure. Which graph represents acceleration (\(a\)) versus distance (\(x\)) variation of this system?