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 implies that the object's velocity changes by equal amounts in equal time intervals.
We need to determine the mathematical relationship between displacement and time to identify the shape of its graph.
Step 2: Key Formula or Approach:
The kinematic equation that connects displacement $s$, initial velocity $u$, uniform acceleration $a$, and time $t$ is $s = ut + \frac{1}{2}at^2$.
Step 3: Detailed Explanation:
In this equation, $u$ and $a$ are constants.
The equation $s = ut + \frac{1}{2}at^2$ shows that displacement $s$ is a quadratic function of time $t$ (due to the $t^2$ term).
In mathematics, any equation of the form $y = Ax^2 + Bx + C$ (with $A \neq 0$) graphically represents a parabola.
Mapping our equation to this standard form, the $y$-axis represents $s$ and the $x$-axis represents $t$.
Because of the quadratic dependence, the resulting curve plotted on a displacement-time graph is a parabola.
Step 4: Final Answer:
The graph between displacement and time for a particle moving with uniform acceleration is a parabola.