Question

Select the graph which represents the motion of a particle along a straight line with uniform acceleration.

• A. Velocity-time graph is horizontal line
• B. Displacement-time graph is horizontal line
• C. Displacement-time graph is straight line
• D. Velocity-time graph is straight line

Hint:

Uniform acceleration always gives a straight line in velocity-time graph and a parabola in displacement-time graph.

Answer 1

The Correct Option is D

Step 1: Understand uniform acceleration.
Uniform acceleration means acceleration is constant with time.

Step 2: Relation between velocity and time.
From kinematics:
\[ v = u + at \]
This shows velocity varies linearly with time.

Step 3: Analyze option (A).
A horizontal velocity-time graph indicates constant velocity, which means zero acceleration. Hence incorrect.

Step 4: Analyze option (B).
A horizontal displacement-time graph means position is constant (no motion), so acceleration is zero. Hence incorrect.

Step 5: Analyze option (C).
A straight line displacement-time graph represents constant velocity, not acceleration. Hence incorrect.

Step 6: Analyze option (D).
A straight line velocity-time graph shows velocity increasing linearly with time, indicating constant acceleration.

Step 7: Final conclusion.
\[ \boxed{\text{Velocity-time graph is a straight line}} \]