Question

The graph between displacement and time for a particle moving with uniform acceleration is a ____.

• A. straight line with a positive slope
• B. parabola
• C. ellipse
• D. straight line parallel to time axis
• E. straight line perpendicular to time axis

Hint:

If the acceleration were zero (uniform velocity), the $t^2$ term would vanish, and the graph would be a straight line. The "curve" in the parabola is the visual evidence of acceleration.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Uniform acceleration means the velocity of the particle is changing at a constant rate. This leads to a non-linear relationship between displacement and time.

Step 2: Key Formula or Approach
The second equation of motion relates displacement ($s$) and time ($t$): \[ s = ut + \frac{1}{2}at^2 \]

Step 3: Detailed Explanation
1. In the equation $s = ut + \frac{1}{2}at^2$, the displacement $s$ is a function of the square of time ($t^2$).
2. Mathematically, any equation of the form $y = Ax^2 + Bx + C$ represents a parabola.
3. Since $s$ is proportional to $t^2$, the graph starts slowly and curves upward as the velocity increases due to acceleration.

Step 4: Final Answer
The displacement-time graph for uniform acceleration is a parabola.