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Velocity-Displacement Graph Analysis

The velocity-displacement graph provided shows a linear relationship between velocity (v) and displacement (x). The graph is a straight line with a negative slope, indicating that as displacement increases, velocity decreases proportionally. This relationship can be expressed mathematically as:

v = -kx + c

where k (slope) and c (intercept) are positive constants.

Key Observations:

• Linear Decay:

  • Velocity decreases linearly as displacement increases.
  • The line passes through the origin (0, 0), so c = 0. Thus, the equation simplifies to:

  v = -kx

  Here, k is a constant representing the rate of decrease.

• Physical Interpretation:
  • This relationship suggests constant deceleration. For a particle under constant deceleration, velocity and displacement are linearly related via: v² = u² - 2as, where u is initial velocity, a is acceleration, and s is displacement.
• Graph Characteristics:
  • Slope: The negative slope (-k) quantifies how rapidly velocity reduces per unit displacement.
  • Axes:
    • Displacement (x): Ranges from minimum (near 0) to maximum (x_max).
    • Velocity (v): Starts at maximum (v₀) when x = 0 and decreases to 0 at x = x_max